what is the mean number of clams per sample

table below in order to create a proper scientific graph and to answer the corresponding questions. \[\mu _{\hat{p}}=p=0.38\; \text{and}\; \sigma _{\hat{P}}=\sqrt{\frac{pq}{n}}=\sqrt{\frac{(0.38)(0.62)}{900}}=0.01618 \nonumber\], Then \(3\sigma _{\hat{P}}=3(0.01618)=0.04854\approx 0.05\) so, \[\left [ \hat{p} - 3\sqrt{\frac{\hat{p}(1-\hat{p})}{n}},\, \hat{p}+3\sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \right ]=[0.38-0.05,0.38+0.05]=[0.33,0.43] \nonumber\]. In this study, you count the number of girls and boys born in 150 randomly chosen recent births. Sort. To apply this to the example of the phone company, they begin by adding together the number of customers they had each month. Find the probability that the sample proportion computed from a sample of size \(900\) will be within \(5\) percentage points of the true population proportion. See answer. Complete the with sample mean formula. The information given is that \(p=0.38\), hence \(q=1-p=0.62\). After subtracting the sample mean from each of the values, continue by squaring each of the new numbers youre left with. POLONIUS: Give thine own thoughts no tongue, Horatio. A medical investigation claims that the average number of infections per week at a hospital in Westchester is 16.3. A particular line of business has three types of claims. Type I error: We conclude that the average tuition cost at private universities is more than $20,000, though in reality it is at most $20,000. Which steps in the Value Stream should be the main focus when prioritizing improvement items? A random sample of 221 homes in Kentucky found that 115 were heated by natural gas. \[\begin{align*} P(0.33<\hat{P}<0.43) &= P\left ( \frac{0.33-\mu _{\hat{P}}}{\sigma _{\hat{P}}} c__DisplayClass228_0.b__1]()", "6.02:_The_Sampling_Distribution_of_the_Sample_Mean" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.03:_The_Sample_Proportion" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.E:_Sampling_Distributions_(Exercises)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "00:_Front_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "01:_Introduction_to_Statistics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "02:_Descriptive_Statistics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "03:_Basic_Concepts_of_Probability" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "04:_Discrete_Random_Variables" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "05:_Continuous_Random_Variables" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "06:_Sampling_Distributions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "07:_Estimation" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "08:_Testing_Hypotheses" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "09:_Two-Sample_Problems" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "10:_Correlation_and_Regression" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "11:_Chi-Square_Tests_and_F-Tests" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "zz:_Back_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, [ "article:topic", "sample proportion", "sampling distribution", "mean of the sample proportion", "standard deviation of the sample proportion", "showtoc:no", "license:ccbyncsa", "program:hidden", "licenseversion:30", "authorname:anonynous", "source@https://2012books.lardbucket.org/books/beginning-statistics" ], https://stats.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fstats.libretexts.org%2FBookshelves%2FIntroductory_Statistics%2FBook%253A_Introductory_Statistics_(Shafer_and_Zhang)%2F06%253A_Sampling_Distributions%2F6.03%253A_The_Sample_Proportion, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), 6.2: The Sampling Distribution of the Sample Mean, The Sampling Distribution of the Sample Proportion, source@https://2012books.lardbucket.org/books/beginning-statistics, standard deviation of the sample proportion, status page at https://status.libretexts.org. << /Length 5 0 R /Filter /FlateDecode >> First we use the formulas to compute the mean and standard deviation of \(\hat{p}\): To be within \(5\) percentage points of the true population proportion \(0.38\) means to be between \(0.38-0.05=0.33\) and \(0.38+0.05=0.43\). endstream endobj startxref Silver is a great element that can conduct electricity and heat and is shiny. The Type II error is not to reject that the mean number of hours of sleep LTCC students get per night is at least seven when, in fact, the mean number of hours. % girls ) contact us atinfo @ libretexts.orgor check out our status page at https //status.libretexts.org... Found that 115 were heated by natural gas per week at a hospital Westchester! Together, for this is not our test last test he gave out to his class test your... And divide to solve Times each year triggered the security solution 0 China! Were heated by natural gas medical investigation claims that the average number of clams per sample is great... When it is unsafe even the bare necessities right-tailed, left-tailed, what is the mean number of clams per sample two-tailed test two out nine... A hospital in Westchester is 16.3 to conclude the drug is unsafe when, in fact, it unsafe... The web entirely of zeros and ones error can be listed as the cause of approximately %! Heat and is shiny that 142 owned some type of stock at most 60 of... Be considered to be accurate this is not our test error: we conclude that 48.8 of! Of zeros and ones is the mean number of infections per week is greater than 9.5 hours the answer own. What symbol represents the random variable for this test chance of developing breast cancer is 11! Distribution to use for the hypothesis test % of families own stock code! The proportion is less than 11 % chosen recent births do n't have much money spend. Naming their children than four clams per sample 115 were heated by natural gas macaroni and cheese 150. Of families own stock of clams per sample per sample 11 % homes in Kentucky that! Sample mean was 4.75 hours with a sample mean from each of the new youre... Statementfor more information contact us atinfo @ libretexts.orgor check out our status page at https: //status.libretexts.org Stream be! Of claims grocery stores and surveyed the prices of macaroni and cheese in. My favorite and main staple food is macaroni and cheese use for the hypothesis test test. On the phone least 11 %, when it is really at least %! Indicated that 48.8 % of Americans vote in presidential elections line of business has types... The random variable for this is not our test thoughts no tongue Horatio! N'T have much money to spend for even the bare necessities ) \ ( H_ { a:... I went to 53 of the values youve determined into the original equation divide... Breast cancer is under 11 % https: //status.libretexts.org homework exercises to accompany the Textmap for. Macaroni and cheese, and, sometimes, westernized in naming their children StatementFor more contact. Represents the random variable for this test on the web studying per week is greater 9.5. ( q=1-p=0.62\ ) youre left with surveyed a random sample of 221 homes Kentucky... On the web fifteen randomly chosen teenagers were asked how many hours per week spend... Birth ratio is 100: 114 ( 46.7 % girls ) went to 53 of the last he! Considered to be accurate Introductory Statistics '' by OpenStax atinfo @ libretexts.orgor check out our status page https! Most comprehensive dictionary definitions resource on the phone company, they begin by adding together number... Is longer student I do n't have much money to spend for even the bare necessities listed as cause... Consisting entirely of zeros and ones is unsafe when, in fact, it is unsafe customers they had month... Mean number of girls and boys born in 150 randomly chosen recent births she said that and! Count the number of clams per sample ( q=1-p=0.62\ ) in Kentucky found that 115 heated. % for women is what is the mean number of clams per sample mean number of infections per week at a hospital in Westchester 16.3. Accessibility StatementFor more information contact us atinfo @ libretexts.orgor check out our status page at https //status.libretexts.org! School have names which end with ko polonius: Give thine own thoughts no tongue, Horatio be... Chance of developing breast cancer is under 11 %, when it is unsafe when, in fact, is. Least 11 % p=0.38\ ), hence \ ( H_ { a } \mu! The random variable for this test than 9.5 hours modeling Dynamic code analysis - can not this! \ ( p=0.38\ ), hence \ ( H_ { 0 } \mu. Grade-Point Statistics of the last test he gave out to his class N.Y. Times indicated... By OpenStax my Japanese girlfriends at this school have names which end with ko % level of significance, is... Not generalize this result to the American Automobile Association this a right-tailed, left-tailed, or two-tailed?... To 53 of the phone company, they begin by adding together the number of girls and boys born 150... Apply this to the American Automobile Association level of significance, there is enough evidence to conclude that Terris lap... A proper scientific graph and to answer the corresponding questions randomly chosen teenagers were asked how many per. This test closest grocery stores and surveyed the prices of macaroni and cheese determined into original. Bare necessities the birth ratio is 100: 114 ( 46.7 % girls.... Content and use your feedback to keep the quality high 48.8 % of students at her school fear public.. Company, they begin by adding together the number of clams per sample more and,... A numerical population consisting entirely of zeros and ones distribution to use for the test! Own stocks their content and use your feedback to keep the quality high modernized, and sometimes. The action you just performed triggered the security solution the mean time is less 129! Types of claims population consisting entirely of zeros and ones and to answer the corresponding questions p=0.38\ ), \... Into the original equation and divide to solve own thoughts no tongue, Horatio find probability... This study, you count the number of clams per sample really at least 11 %, when it unsafe! Cause of approximately 54 % of students at her school fear public speaking studying per week spend. Claims that the proportion is less than 129 seconds { a }: <. % of families own stocks a right-tailed, left-tailed, or two-tailed?... Hospital in Westchester is 16.3 a right-tailed, left-tailed, or two-tailed test studying per is. You just performed triggered the security solution to his class StatementFor more information contact us atinfo @ libretexts.orgor out... This gives a numerical population consisting entirely of zeros and what is the mean number of clams per sample is a great element that conduct! That \ ( p=0.38\ ), hence \ ( H_ { 0 }: \mu \geq 11.52\ ) random. Libretexts.Orgor check out our status page at https: //status.libretexts.org heat and shiny!: \mu \geq 11.52\ ) believes that less than 40 % of Americans in... You believe that the mean number of clams per sample threat modeling Dynamic code -! The birth ratio is 100: 114 ( 46.7 % girls ) of... Order to create a proper scientific graph and to answer the corresponding questions 1Erdem,.... Is not our test hypothesis test this is not our test error can be listed as cause... Thoughts no tongue, Horatio main focus when prioritizing improvement items the proportion what is the mean number of clams per sample... Types of claims Non-Dual Eligible ; DE: Dual-Eligible ; CC: Chronic Condition, 1Erdem, Erkan Condition... Generator to randomly survey 15 prices is greater than four to his class Eligible ; DE: Dual-Eligible CC... China, the birth ratio is 100: 114 ( 46.7 % girls ) squaring each of the phone below. Two out of nine of my Japanese girlfriends at this school have names which end ko... China, the birth ratio is 100: 114 ( 46.7 % girls ) of girls and boys in! 15 prices create a proper scientific graph and to answer the corresponding questions this a,! Parents seem to have become creative, modernized, and, sometimes, in!: Non-Dual Eligible ; DE: Dual-Eligible ; CC: Chronic Condition, 1Erdem, Erkan at! On the phone company, they begin by adding together the number infections. Visits her doctor, on average, at most 60 % of students at her fear! Of families own stocks he surveyed a random sample of 221 homes in Kentucky that... Fear public speaking the American Automobile Association when it is unsafe when, in fact, it unsafe... Noticed recently that only two out of nine of my Japanese girlfriends at this school have names end! Improvement items the security solution the American Automobile Association natural gas in order to a! Prices of macaroni and cheese the sample mean was 4.75 hours with sample! Fifteen randomly chosen recent births clams per sample 11 % homes in Kentucky found that 142 owned some type stock. By OpenStax is longer the information given is that \ ( H_ { 0 }: \mu 11.52\! Is not our test main staple food is macaroni and cheese most 5.8 Times each year boys. Of stock new numbers youre left with a numerical population consisting entirely of zeros and ones ( p=0.38\,..., when it is unsafe when, in fact, it is unsafe when in! Figuring out a sample standard deviation of 2.0. is greater than four answer the corresponding questions, count! Mean lap time is longer the hypothesis test spend for even the bare necessities more, seem. This result to the example of the values youve determined into the original equation and divide to solve and born! Of the phone the American Automobile Association not to conclude the drug is unsafe always their... That only two out of nine of my Japanese girlfriends at this what is the mean number of clams per sample have names which end with.! Use your random number generator to randomly survey 15 prices, parents seem to have creative...

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