So Zen's central notion of the individual-inseparable-from-the-world is consistent with behavior analysis and evolutionary biology. When contingencies are the units of analysis, the individual is part of an interactive context. Just as important, behavior analysis and Zen preserve no subject–object distinction. To step back from agency accounts ( Vargas, 1996) and explanations “that appeal to events taking place somewhere else, at some other level of observation, described in different terms” ( Skinner, 1950, p. 193) is to step toward Zen. Whether behavior analysts find these issues interesting or not, one thing is certain: Mentalism is uniquely ill suited for dealing with Zen's extreme parsimony. The goal is not to create a reductionist or operationalist thesaurus but rather to discover what grows in the estuary made by Zen and behavior analysis rather than Zen Buddhism and radical behaviorism. Unlike most other analyses of Eastern philosophy, this one will not follow the formula “their term X = our theoretical term Y” (e.g., Jung, 1959 Rosen & Crouse, 2000) or “our neurological event Y” (e.g., Austin, 1998 Bagchi & Wenger, 1957 Kasamatsu & Hirai, 1966 West, 1987). The unique repertoire called Enlightenment has been reported for 2,500 years and, if Zen Enlightenment results from behavioral processes, behavior analysis must apply. 1977): “Everything you know is wrong.” What I've learned since is that in Zen's case, anything you know is wrong. And that reminded me of something Richard Malott said at the start of his principles of behavior lectures (ca. There was antimatter, a parallel universe where verbal distinctions move one farther from Zen, not closer to knowledge, as with behavior analysis. 2 Zen took me outside not just culture-bound distinctions but also distinctions themselves. I'd barely begun luxuriating in the comfortable notion that verbal behavior is epistemology's headwaters when years of meditating yielded a complementary insight, Samādhi. Digesting his remarks led me to the giddy epiphany that Verbal Behavior (1957) was the unified field theory of academe-Skinner's analysis accomplished for human behavior what Einstein had sought for physics. In what followed, he redirected my attention to verbal behavior, of which philosophy is a subset. She called his adjoining office and said “Someone here would like to meet you.”Īfter I nervously posed my questions, he leaned back, looked up for about 5 seconds, resumed a normal posture and said “I don't care much for isms.” I told her I had a question for Skinner regarding behaviorism. Dissatisfied with answers that professors, books, and journals provided, my wife and I drove to Cambridge, Massachusetts, where I hiked to the 7th floor of William James Hall and knocked on Skinner's door (actually his secretary's door). I was struggling to find good answers for epistemological questions (e.g., were private events, in some important way, dualistic, possibly epiphenomenal? Did Richard Rorty's, 1965, eliminative materialism fit a behavioral view better than other monistic accounts being given?). A more profitable approach to the relation between Zen and behavior analysis was implied in a conversation I had with B. Philosophies, especially philosophies of science, are foundations built under existing logical structures (e.g., Mach's positivism addressed Newtonian mechanics logical positivism and operationalism, Einstein's relativity theory etc.) and contribute little to the field per se. 1 Discussion regarding the Eightfold Way, reincarnation, free will, and so on are about Buddhism, but they are not Zen any more than About Behaviorism ( Skinner, 1976) is applied behavior analysis. Zen is neither of those things it is the outcome of Zen practices. Should that conversation be continued? I will argue the affirmative with, it seems to me, the greater profit going to the behavior analyst.īehavior analysts have addressed Buddhism broadly defined (e.g., Baum, 1995 Diller & Lattal, 2008 Williams, 1986) as a philosophy or religion. Conversely, a behavior analyst might argue that understanding Hamlet's statement requires a functional analysis of the conditions under which it was learned and used, and there is nothing special about the or neither. If Shakespeare had been a Zen Buddhist, Hamlet's famous soliloquy might have begun “To be or not to be, or neither.” How is such a statement to be understood?Ī Zen monk might say that Hamlet's first two options exemplify the illusory distinctions cultures regularly transmit, but adding the or neither shows that he has moved beyond a verbally framed normal-life worldview and is edging toward Zen-and thus, possibly, Enlightenment.
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# Use Ledger Nano Device With WX Network App Press both left and right buttons simultaneously to launch the app. Once the Waves application is installed, use the left or right button to find it on the dashboard. # Open Waves app on your Ledger Nano Device then the app installation will be finished. The installation window will appear and your Ledger Nano device will display Processing. In the Ledger Live catalog, find Waves app and click Install. If asked, allow the manager on your device by pressing the right button. Open the Manager in Ledger Live (opens new window).Ĭonnect and unlock your Ledger Nano device. Google Chrome, Firefox browser or WX Network Desktop app is installed. The latest firmware is installed (opens new window). Note: WX Network supports Ledger Nano S and Ledger Nano X models. You've initialized (opens new window) your Ledger Nano device. Please email us at or join the Stacks Discord if you have any issues while using your Ledger device with the Hiro Wallet.# Use Ledger Nano Devices With WX Network # Prerequisites Select "Approve" on your Ledger device to confirm and broadcast the transaction.Select "Sign transaction" and verify the address and all other relevant transaction details as displayed on your Ledger device. Select "Preview" then "Sign transaction and send" to initiate the transaction.Enter the address to which you'd like to send STX, the amount of STX and an optional memo describing the transfer.Select "Send" at the top of the window under your total balance.Copy the address shown in the Hiro Wallet to receive STX from it.Verify that the address shown in the Hiro Wallet matches the one shown on your Ledger device and select "Approve".Select "Receive" at the top of the window under your total balance.Select "Approve" on your Ledger device to proceed with using the Hiro Wallet.Your total balance is shown at the top of the window under "Total balance".Select "Continue" to view the receive address on your Ledger device.Open the Stacks app on your Ledger device.Connect your Ledger and enter its PIN on the device.You'll need to transfer your recovery phrase to a separate Nano S or X device. Ledger Blue is not supported by the Hiro Wallet.Press both top buttons on your Ledger device simultaneously to proceed whenever it shows "Pending Ledger review" on the screen.If you don't see the upgrade option, turn off "Developer Mode" before proceeding. Don't turn on "Developer Mode" before upgrading your firmware, otherwise Ledger Live won't show you the dialog to upgrade.Return to Hiro Wallet and proceed with authentication.Confirm "Allow Ledger manager" on device.Connect and enter your PIN on your Ledger device.Go to "Manager" on the left-hand side of Ledger Live.Select "Settings" in the top-right corner of Ledger Live then the "Experimental features" tab.Upgrade your firmware for Ledger Nano S to version 1.6.1 or Nano X to version 1.2.4-5 or greater.You'll need to install it there before proceeding to connect your Ledger Nano S or X device to the Hiro Wallet for authentication. The Stacks app is available in Ledger Live. The Stacks app for Ledger empowers users to connect their Ledger devices to the Hiro Wallet (MacOS, Windows and Linux) for securely managing their STX holdings and participating in Stacking. Once you've authenticated into the Hiro Wallet with either your Secret Key or hardware device, you'll see an option on the right-hand side of the home screen to "Get started" with Stacking: If you've decided to Stack directly through the Hiro Wallet, see the steps for participation below. After your chosen Stacking duration, you’ll have to wait one cycle before you can stack from the same address again, regardless of how many cycles you stacked The amount of STX required to participate has been steadily increasing since Stacking was initiated on mainnet.Ģ) Stacking is irreversible and once STX tokens are locked, they will not unlock even if the dynamic minimum increases and the STX are no longer eligible for rewards.ģ) There is a "cool down" cycle between Stacking cycles. Stacking is otherwise available through one of our partners at /stacking.Ī few things to note when Stacking directly: 1) Stacking directly requires meeting a dynamic minimum threshold of STX that changes based on participation. To participate in Stacking directly via the Hiro Wallet, you'll need at least the minimum number of STX in your Hiro Wallet balance. Best iPhone Screen Protector: ZAGG InvisibleShield Glass Elite VisionGuard They’re also a lot smoother to the touch, which is pretty essential when using a touchscreen.Īlthough they’re not reusable, some brands include spares with each purchase in case you make a mistake during the installation process, or the protector acquires too many scratches. They provide better protection, they’re fingerprint-resistant, and they make for a much clearer viewing experience. Tempered glass screen protectors are just the opposite. Considering the amount of wear they take over time, though, you probably won’t want to reuse them anyway. Really, the only thing plastic screen protectors have going for them is that they’re reusable. They also don’t protect the edges of the screen. A plastic screen protector will lose its clarity over time: combined with the fact that they’re not fingerprint-resistant, count on a smudgy viewing experience. For one thing, they’re thinner, so they provide less protection and scratches show more clearly. There are several notable downsides to plastic screen protectors. Look for a tempered glass screen protector instead of one made from plastic. $89.99 Buy on Amazon Last updated: at 17:41 Tempered Glass Screen Protectors In the end, screen protectors are mainly designed to guard against scratches and fingerprints, while adding a little additional drop protection. It’s intended to be sacrificial, so plan to swap it out for a new one eventually. Scratches and cracks can still appear, but it’s the protector being damaged, not your expensive phone display. Keep in mind the screen protector itself isn’t invincible. Sand can also scratch iPhone screens, so if you’re likely to spend time on the beach, a screen protector is a small, worthwhile investment. They also tend to ward off oily fingerprints, and some include antibacterial technology that kills the common surface bacteria living and breeding on your phone. Scratches remain a concern, though, especially if you keep your phone in a pocket, purse, or bag with metal items like keys or coins. Unless you’re bungee jumping or trying your hand at parkour, you likely won’t be doing things that risk shattering your screen. The glass on recent iPhone models is extremely tough, persevering through damage test after damage test (until dropped from 10 feet, at least.) Along with flip phones, VCRs, and classic iPods, shattered iPhone screens are becoming a thing of the past. In British English, if you’re “pissed off” then you’re angry. I was so pissed last night, I can’t remember anything about it. But when British people are “pissed”, they’re drunk! When Americans say they’re “pissed” they mean they’re angry. In British English, you can refer to your friends as your mates. Those lads next door make a lot of noise don’t they? 8. “Lad” is a bit like “bloke” because it refers to a man, but in this case, a young man. You’re probably familiar with “hi”, but in the UK people often say “hiya” instead. But in British English “cheers” can also mean “thank you”. In all parts of the English-speaking world, people say cheers as a toast before drinking. You use “bloody” to emphasise what you're saying – a bit like “very” but more offensive! You often use it when you're angry. It can also refer to a female partner or girlfriend. If someone says “alright?” with a rising intonation, they’re asking “how are you?”. This is a great place to start a list of British slang phrases as you’ll hear it all the time in the UK. And help you understand their conversations better! Top 10 British Slang Phrasesĭon't have much time? Want to learn the top British slang words you’ll hear all the time in the UK? Check out this list for the top ten. In this post, you'll discover 67 British slang phrases that will help you impress your British friends. While many British people understand and use American slang due to the influence of US culture, the UK has its own unique slang words and expressions. Then learning British slang phrases will help! Do you live in the UK and want to catch what British people are saying? Do you want to understand British TV shows like “Peaky Blinders”, “Sherlock” or “The Office”. Ĭheck for, and if available, update your os Then uninstall the cc desktop app, again using the correct uninstaller per. Uninstall every cc app including preferences per If that fails, do a clean cc install carefully following each applicable step: If that fails, uninstall using the correct uninstaller from. Please click here to purchase.Reset the cc desktop app by making sure it's in the foreground, then press: Students can lease a license the software for their personal computers at a discounted rate of 60%.Adjunct Faculty can download the Adobe Creative Cloud to their personal device. Core + Adjunct Faculty and Staff receive the software on their Lesley issued computer and have work from home rights on 1 additional personal computer.Is There An Educational Discount For My Personal Computer? NOTE: The address you enter will be your Adobe ID, so use a frequently used address that you’ll remember. You may have to wait for some time before receiving the email. You will receive a mail from Adobe with a link to verify your email address. Go to Adobe accounts and click Get an Adobe ID.įollow the instructions and enter a valid email address. You won't need an Adobe subscription to use the software on campus devices, but Adobe does require an account to log into the software to use it. Students will need to create a free Adobe ID. Student's can access the software in all computer classrooms, open computer labs, and library on campus. *Associated costs are a departmental expense. Paid professional development on Adobe applications is available through the vendor New Horizons. Adobe's YouTube Channel contains useful getting started tips and tricks.Adobe offers free online courses through their Adobe Education Exchange portal.How Do I Get Training On Adobe Creative Cloud Applications? Access to Adobe Stock is a departmental purchase. The full list can be viewed at: Īdobe Stock is not included as part of our volume license. What Applications Come With Adobe Creative Cloud?Īll of the following applications are available to be installed on your computer. If you have a laptop a technician will either connect remotely or you can schedule an appointment to drop off your computer. Desktop installations will be performed remotely in order to quickly roll out the software to as many individuals as possible. The software can be installed remotely by a technician. The installation process takes about 1.5 hours to install every application. How Long Does It Take To Install The Software? We will address requests for installation in the order they are received. We appreciate your patience while we prioritize all requests for support. You can submit your request by emailing Quickly Will My Request Be Fulfilled? If you would like software installed on your computer, you can submit a request by e-mailing IT for installation assistance for your Lesley issued computer. For an individual who doesn’t perform such tasks as part of their essential job functions, the entire suite of applications would take up a significant as well as unnecessary amount of storage space and system resources on a computer. If you don’t currently perform any of the aforementioned tasks, we don’t recommend having the application installed. What Is Adobe Creative Cloud and Do I Need It?Īdobe Creative Cloud is a collection of software for graphic design, video editing, web development, and photography. Individuals who need access to the suite of applications, and have an existing computer, can submit a request for installation. Like Microsoft Office, Adobe Creative Cloud will be pre-installed on all newly deployed computers going forward. Adobe Creative Cloud is now a part of the standard suite of applications available for installation on all Lesley University owned computers. If we had to give out awards, side bangs would definitely win most popular, but theyre especially flattering on round faces, which are soft around the. Ĭhoose your face shape and find the best hairstyles that suits you. Best for Round Face Shapes: Sideswept Bangs. The basic seven male and female shapes are given below. The main features of this application is the hairstyling tips, for female of different face shapes to make your face shape clear, whichever shape it is, look balanced and proportionate. Whichever category you fit into, there are simple things you can do to enhance your best features and bring forward your best 'you.' Hairstyles with height and fullness at the crown will give the illusion of a narrower face shape, particularly those short in length. If you have a round face shape, the object is to add length and avoid width. The Right Hairstyle for Your Round Face Shape. And though many people may not have thought about the shape of their face, there are many whose faces have characteristics they don't love. If you have an oval shaped face then lucky you, we are super jealous because most hairstyles will suit you Experiment with short lengths, tapered bobs. Hairstyles with straight across bangs will work to shorten long faces, as will side parts. Though every person's face is unique, it's generally accepted that there are six basic face shapes. This app explains how to choose the right hairstyle depending on you face shape. If you want a short haircut and have a round face shape, consider a pixie cut. This creates a more vivid and true representation of the various hairstyles. I love how the editing tools allow me to move and stretch hairstyles and colors to fit my pictures. By far, the most flattering haircuts for women with round faces are those that add definition and shape. Title: Great Editing Features Allow Real-Life Looks You would need to know your shape of face for finding “the right” haircut or hairstyle. This app will help you to identify your face shape and check a lot of different hairstyles. Have you ever had a question "What hairstyle is better for my face shape?". However, try to avoid styles that stick straight up, as you don’t want to look overly boxy. Which hairstyle is better for your face shape? This app identifies your face shape to try on a lot of different hairstyles that suits you. What to avoid: Luckily, most hairstyles will look good with a square face shape. This article was first published on 18 April 2020 and was updated on 9 February 2021. To read other interesting Electronics basics: click here There are many different types of electrical switches. We’ll start out with electrical switches. NPN Bipolar Transistor/ PNP Bipolar Transistorĭefinition of a Transistor: It is a semiconductor device used to amplify or switch electronic signals and electrical power. Here are the electrical symbols including communications symbols like phones, doorbells, and security systems. Power Supply SymbolsĬontrolled voltage source/Controlled Current sourceĪC voltage source/Generator Meter Symbolsĭefinition of a LED: It is a semiconductor device that emits light when an electric current is passed through it. This is not a definitive list of all symbols used in electrical identification, but merely a guide to some of the more commonly used symbols. Export it to Microsoft Word ®, Excel ®, PDF, or PowerPoint ® with a single click. Reposition them on the page and SmartDraw will keep them connected, automatically. Click and stamp electrical symbols onto your layout. You can learn more about Antenna and their basics. Just select a template and start customizing. Antenna Symbolsĭefinition of an Antenna: An electrical device converts electric power into radio waves and vice versa. Capacitor Symbolsĭefinition of a Capacitor: It is a device that stores electrical energy in an electric field. Photoresistor / Light-dependent resistor (LDR)ĭefinition of a Resistor: As the name suggests, they resist the flow of excessive electrical power or voltage passing through the circuit, in a precise and controlled manner. Variable Resistor / Rheostat (IEEE)/(IEC) The term refers to the working drawing used by the architectural, engineering, and construction professions to represent the desired construction plans. Relays switches are used to open and close circuits electromechanically or electronically. A blueprintis a photographic print of a prepared drawing with the lines and lettering in white on a bright blue back- ground it’s used for mechanical, electrical, and architectural drawings. Lamp/Light Bulb Symbolsĭefinition of a Relay: It controls circuits by opening and closing contacts in another circuit. You can learn more about the Basics of Inductors. There is a circuit symbol for each and every electrical component or device used in a circuit such as passive components, active components, measuring instruments, logic gates, etc.Ī few electronic symbols that can be used in the circuit diagrams are given below for reference: Wire Symbolsĭigital/Common Ground Inductor/Coil Symbolsĭefinition of an Inductor: It is a device that temporarily stores energy in the form of a magnetic field. the circuit on a breadboard or assembled printed circuit board) This enables anyone to read electrical circuits or Electrical schematic diagrams and floor plans with ease and clarity.Įlectrical symbols represent the components of electrical and electronic circuits and do not define any function or process unless the circuit is implemented with components being physically used. Though electrical symbols are standardized, they may vary from country to country, or engineering disciplines, based on traditional conventions. Some of that included the spiritual follow-up to Pirate’s Hook called Safari Ranger and a Kinect-enabled game called Treasure Hunt which combines some elements of a game like Temple Run with some character designs similar to what you would see in a Super Mario Bros. It can support up to 16 locally linked game cabinets for 8v8 team play and will be available in the Deluxe (above) and Standard (below) cabinet configurations, which take up the space of a typical 42″ driver.ĪR was the main video-only game on their booth, otherwise UNIS’s main focus was on redemption/videmption. Strafing would be nice although I am not sure how that can be implemented without a hardware control change just turning left to right a little faster would probably be sufficient. That threw me off a little for aiming however the game does have some auto-aim shots going on to help you along. The controls use a simple joystick (for aiming and firing) and throttle (for speed and transforming) combination, the main suggestion I could think of for improvement would be for your machine to turn faster and to have the enemy position compass adjusted so it is not directly in the center of your target reticule. Much like Unreal Tournament, the game announces streaks like “Double-kill” “Multi-kill” “Rampage!” as well as announcing headshots. There are only three arenas, I will need to check to see if any future updates will add more. The obvious comparison is to a Transformers video game, which we have in the industry but as a light-gun shooter.Īrmed Resistance plays solidly without any frame rate issues to speak of. One interesting feature is the ability to transform between a walking robot mech suit and a vehicle by the push of a button. The team with the most points at the end of the match wins. The goal of the game is pretty straightforward, capture the enemy base’s to win while protecting your own. This arena-based 3rd person shooter is something of a rarity in the modern arcade industry, the likes of which we haven’t seen since games like Sega’s Outtrigger and Atari’s War: Final Assault. One game I have been looking forward to playing was Universal Space’s Armed Resistance. UNIS – Universal Space has generally featured large booths at every trade show where I have seen them but they had quite a line-up of brand new redemption content that had not been seen previously to show for IAAPA 2014. They also did have Temple Run 2 on hand and a complete redesign of the SharpShooter cabinet: This one is controlled by a joystick instead of a trackball. SSA is an endless runner type game where your character automatically runs along collecting things. I didn’t get a chance to play yet but taking just a quick visual look I say it looks really nice.Ĭoastal Amusements – The up-front focus at the Coastal booth was on their new Yahtzee videmption game (which I apparently forgot to snap a picture of) and Subway Surfers, which we covered a little while ago. The two cabinets on hand were being played when I walked by and I didn’t have a chance to try it so I will follow-up with impressions on this one but again, I wasn’t sure if this game was going to be at the show, much less at the Benchmark booth.Ĭhicago Gaming – I wasn’t sure if the new and highly anticipated Medieval Madness Pinball Remake was going to be at the show but here it is in all its glory. As it so happens, they have Tecnoplay’s Mini Motor Racing Arcade there, you can read previous coverage on this game here. They normally focus on creating popular mechnical redemption games like Monster Drop but they are starting to dabble in video and videmption games. It should be noted that I did not see BattleShip there, which was at Amusement Expo 2014.īenchmark Games – One big surprise I stumbled upon was at the Benchmark Games booth. As such, it is Flappy Bird with a big screen and the backlit LED translucent plastics. This was released a short time ago and has been showing up at certain venues already. If you haven’t already, here is part 1 of my IAAPA coverage.īaytek – Yesterday I only managed a quick walk past the Baytek booth where I caught the new Flappy Bird Arcade. As mentioned last night, I had much more to post but I just did not have the time to get to it all unfortunately. Which makes sense considering studio Bones is behind this title and they have a lot of experience in taking a running manga and both faithfully adapting it to the screen while also cleaning up scenes to flow smoother into the overall narrative. There are pitfalls in the story, but its one of the tighter shounen shows I’ve seen in a long time. There’s a lot to like about this show, from the brisk pace to the enjoyable characters to the interesting world that seems simple at first but quickly fleshes out to a more complex setting that forces the themes of what it is to be a hero into the spotlight frequently. But not only is there some stable world building, but the characters, from the leads to the supporting cast, have all had amazing arcs and growth over time. I was shocked with how much I enjoyed it, especially considering the genre it is, which isn’t known to have stable character progression. When I first tried this show out, it was already just starting the third season’s stream. Religion has not really come into play at all thus far. It’s a very quick scene, thankfully.Īside from ideals about justice and heroism, nothing to note here. There is also a spa scene in season three where the girls are covered by nothing besides, well, mist. They are aren’t very common, considering how many characters have outfits ripe for it, but it does happen now and again. While the show attempts to address the practicality of these outfits (some quirks relay on skin contact, for example) the show does take advantage of these moments for some fanservice shots. One common character has a v cut all the way to her waist. A few female characters have suggestive and very tight hero outfits. This really comes down to the costumes primarily. When he doesn’t say much, the language is pretty tame, but in episodes heavily featuring him it can spike a bit. I haven’t noticed the dub being worse than the original so it all comes down to how many lines that one character has in the episode. Almost all instances come from one ever angry character. If Fullmetal Alchemist violence bugs you, this might not be the show for you.ĭ-mn is the most common, but a few sh-ts and b-words. Especially with our lead, who gets into dangerous and harmful scenarios a lot. So blood, broken bones and bruises occur a lot. This is a typical shounen show violence wise. At least that’s what he fears until running into his idol, pro hero All Might. Because of this, his dream of becoming a professional hero is just not in the cards. Izuku Midoriya is one of very few children born without a “quirk,” special abilities nearly every human on the planet has. Genres: Action, fantasy, science fiction, drama Even if science fiction isn’t your usual go-to, this is well worth a watch. If you want to take a break from TV series for a bit, I recommend looking into your local library or digging around Amazon for this one. The plot twists are pretty solid as well and make for a pretty impactful ending. The two leads also have a pretty organic relationship, which is nice amidst all the rushed ones rampant in more recent films. The characters are well crafted and although we only have one film to get to know them, we are given enough context and dialog to get a sense of what drives them and what they fear. While the story itself isn’t overly complex, the way it is presented cinematically is amazing (although, the switching of the camera angle between gravitational pulls can be very disorienting so be warned on that). It’s one of the better science fiction films I’ve seen in awhile, not just in the realm of anime but in general. This belief keeps many people in line with the government and is a plot point, so it can’t be easily ignored. The people in one of the “worlds” consider those who’s gravity is reversed to be “sinners” and that they deserve to float into the sky and die as it is divine punishment from God. There is a villain who makes some rather suggestive remarks towards the lead, but nothing is shown or occurs (besides being creepy). Some d-mns and one or two b-words, but nothing excessive. Not quite as bad as FMA, but still not for younger audiences. Near the end we see quite a lot of blood from a few gun and knife wounds. Wishing to explore more of her small underground world, Patema ignores the advice of her elders and ventures deeper into the tunnels where gravity seems to be reversed…Ī few characters are injured and some killed. Patema lives in a world years after an experimental failure at controlling gravity caused much of the earth to float away into the sky, never to return. The value given by a z-table using a z-score of -2.36 is 0.0091, which, when doubled, is 0.0182 or approximately 0.02. Since the alternative hypothesis is not specific about the population mean being either greater than or less than the value in the null hypothesis, we have to consider both tails of the distribution, but by symmetry of the standard normal distribution, we can accomplish this by simply doubling the value we get from using our obtained z-score with a z-table. Taking the difference between our sample mean and the population mean and dividing it by the standard error gives us our z-score (number of standard errors our sample mean is away from the population mean), which is approximately (7.36 - 7.4) / 0.01697 or -2.36. In our example, the standard error of the mean therefore has a value of 0.12 / 50^0.5, or approximately 0.01697. I say would, because unfortunately, we don’t always know the population standard deviation, and so (as it seems they did here, despite knowing the population standard deviation), we are using the sample standard deviation in its place to find an estimate of the standard deviation for the sampling distribution of the sample mean, which is also known as the standard error of the mean. That would give us a standard deviation for the sampling distribution of the sample mean. Since the answer to what we are asking comes from the sampling distribution of the sample mean, we would find the appropriate standard deviation to use by dividing the population standard deviation by the square root of the sample size (since the variance of the sampling distribution is the population variance divided by the sample size, and the standard deviation is the square root of the variance). To use a z-table, we'll need to find the appropriate z-score first. (We could also use a t-table, but it is allowable to just use a z table since our sample size is larger than 30) So now, we can use the normal cumulative density function or a z-table to find this probability. Under that assumption, and noting also that we are given that the population is normally distributed (or that we took a sample size of at least 30 ), we can treat the sampling distribution of the sample mean as a normal distribution. The p-value is the probability of a statistic at least as deviant as ours occurring under the assumption that the null hypothesis is true. |
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