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# hypothesis testing exercises and solutions

Solution: Sample size n =50 Sample mean = 10 km Sample standard deviation s = 3.5 km . 4 Hypothesis Testing Formally examine two opposing conjectures (hypotheses), H 0 and H A These two hypotheses are mutually exclusive and exhaustive so that one is true to the exclusion of the other We accumulate evidence – collect and analyze sample information –for the :purpose of determining which of Conduct a hypothesis test. A survey of 22 LTCC Intermediate Algebra students generated a mean of 7.24 hours with a standard deviation of 1.93 hours. At $$\alpha = 0.05$$ level, is the class’ mean family size greater than the national average? We can reject, or fail to reject, the null hypothesis just based on an inspection of the Estimating a P-value from a simulation. NOTE: For more accurate results, use more California community colleges and this past year's data. Hypotheses: H 0:μ=140 H A: μ>140 4.Test Statistic: = = =2.78 Text Book : Basic Concepts and Methodology for the Health Sciences 23 n s X Z o-P 157 27 146 140 2.1548 6. Conduct a hypothesis test to see if your decision and conclusion would change if your belief were that the brown trout’s mean I.Q. Recently, many groups have been studying whether or not the women's movement has, in fact, resulted in an increase in the average work week for women (combining employment and at-home work). of a set of brown trout. Let $$\bar{X} =$$ the mean number of bubbles per blow. A poll done for Newsweek found that 13% of Americans have seen or sensed the presence of an angel. Does the evidence support the claim for Kentucky at the $$\alpha = 0.05$$ level in Kentucky? H 0: μ=52 H a: μ>52 α==.05, 1.65zcritical z*=1.78 (This test statistic lies in the Rejection Region for H o.) Type I error: We conclude that the mean number of cars a person owns in his or her lifetime is more than 10, when in reality it is not more than 10. Twenty-nine percent of high school seniors get drunk each month. At the $$\alpha = 0.10$$ level, is the Austin, TX commute significantly less than the mean commute time for the 15 largest US cities? The scores of people in general on this measure are normally distributed with a mean of 19 and a standard deviation of 4. Conduct a hypothesis test. An F test of the joint hypothesis that the optimal values for p and a, respectively, are 2 and 40, yields a p-value of 0.180. State a consequence of committing a Type II error. The distribution of the population is approximately normal RobustRobust: : These hyp. Question 16A newly developed muesli contains five types of seeds (A, B, C, D and E). A random sample of 221 homes in Kentucky found that 115 were heated by natural gas. The sample mean was 18.1 with a sample standard deviation of 1.3. Type I error: We conclude that the mean is not 34 years, when it really is 34 years. by Nedda Misherghi and Rachelle Hall. At a significance level of $$a = 0.05$$, what is the correct conclusion? Type II error: We conclude that 5% or more adults ride the bus to work in Los Angeles when, in fact, fewer that 5% do. At the 5% level of significance, there is not enough evidence to conclude that a woman visits her doctor, on average, more than 5.8 times a year. YEAR 3. Here is a list hypothesis testing exercises and solutions. Am I right? 1. The mean number of cars a person owns in his or her lifetime is not more than ten. In America, most nursing mothers wean their children much earlier. In chapter 7, we will be looking at the situation when a simple random sample is taken from a large population with unknown mean and standard deviation. Every hypothesis-testing situation begins with the statement of a hypothesis. To use an inferential method called a hypothesis test To analyze evidence that data provide To make decisions based on data Major Methods for Making Statistical Inferences about a Population The traditional Method The p-value Method Confidence Interval . Members of a personnel department do not believe this figure. After four years the girls were surveyed again. For each question below, consider the following question: To use an inferential method called a hypothesis test To analyze evidence that data provide To make decisions based on data Major Methods for Making Statistical Inferences about a Population The traditional Method The p-value Method Confidence Interval . Type I error: We conclude that the proportion of high school seniors who get drunk each month is not 29%, when it really is 29%. A statistical hypothesis is a conjecture about a population parameter. Population mean μ = 9.5 km. (Horatio exits, followed by Polonius, leaving Hamlet to ponder alone. The organization thinks that, currently, the mean is higher. tests are those that produce fairly accurate results even when the data suggest that the ppp g population might not meet some of the assumptions. 2. In Exercise, the P-value for a hypothesis test is shown. Type II error: We conclude that the average tuition cost at private universities is at most $20,000 when, in fact, it is more than$20,000. C’mon please, mom, please, what the hell. State the null and alternative hypothesis. Use your random number generator to randomly survey 15 prices. Show the formula set-up. There is sufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is less than 20%. You decide to check this out on your own. Suppose the null hypothesis is “the drug is unsafe.” What is the Type II Error? Type II error: We conclude that the proportion of women who develop breast cancer is at least 11%, when in fact it is less than 11%. 3. If the P-Value is less than or equal to a certain predefined threshold (the significance level), we will reject the null Hypothesis. HORATIO (to Hamlet): What should we do, my Lord? Confidence Interval: $$(0.0502, 0.2070)$$: The “plus-4s” confidence interval (see chapter 8) is $$(0.0676, 0.2297)$$. Did the medication affect intelligence?View Solution to Question 1. Use $$\alpha = 0.01$$ level of significance. 27 November, 2015 - 16:22 . The student academic group on a college campus claims that freshman students study at least 2.5 hours per day, on average. Question 18A publisher is interested in determing whinf of three book cover is most attractive. In hypothesis testing, the following rules are used to either reject or accept the hypothesis given a . For that same year, a survey was conducted of 41 California registered nurses to determine if the annual salary is higher than $69,110 for California nurses. This conjecture may or may not be true. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. Lecture 5 Class Exercises- SOLUTIONS Hypothesis Testing: Paired and Independent Samples Case Study A 1. Hypothesis Testing Using a P-Value In Exercises 31-36, (a) identify the claim and state Ho and Ha. 5. Use the test statistic to determine the p-value. (c) find the corresponding P-value. At the 5% significance level, there is enough evidence to conclude that the mean amount of summer rain in the northeaster US is less than 11.52 inches, on average. Type I error: We conclude that the mean starting salary is less than$100,000, when it really is at least $100,000. Hypothesis Testing Problems And Solutions Hypothesis Testing Solved Examples (Questions and Solutions) by March 11, 2018. Thus, the value of the test statistic is Since and , we have that In other words, the test statistic does not exceed the critical values of the test. In order to carry out the test, we need to compute the test statistic where is the sample size, is the value of the variance under the null hypothesis, and is the unadjusted sample variance. Private universities mean tuition cost is more than$20,000 per year. Refer to Exercise 9.119. Then you review fundamental statistical concepts, such as the sampling distribution of a mean, hypothesis testing, p-values, and confidence intervals. Q1. Again, null hypothesis testing is the most common approach to inferential statistics in psychology. Come Horatio, let us go together, for this is not our test. Solution 1. Assumption: population is not normal, σ2 is unknown 3. We all get together from different towns. Let $$\bar{X} =$$ the average cost of a daily newspaper. "The Problem with Angels," by Cyndy Dowling. Here is a list hypothesis testing exercises and solutions. The smaller the P-value, the more strong the evidence in favor of our alternative Hypothesis. Based on the results that follow, should she count on the mean work week to be shorter than 60 hours? Each of 10 cars was first filled with regular or premium gas, decided by a coin toss, and the mileage for the tank was recorded. Normal hypothesis test for population proportion Hypothesis test for population mean Type I and Type II errors REQUIRED DATASET: IPUMS-International REQUIRED VARIABLES: 1. A student believes that less than 40% of students at her school fear public speaking. The distribution to be used for this test is $$\bar{X} \sim$$ ________________. (Polonius turns to Hamlet.) Elementary Statistics (12th Edition) answers to Chapter 8 - Hypothesis Testing - Review - Review Exercises - Page 434 7 including work step by step written by community members like you. Does the Almanac result remain valid? Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Hypothesis Testing Problems And Solutions Hypothesis Testing Solved Examples (Questions and Solutions) by March 11, 2018. Hypothesis Testing is basically an assumption that we make about the population parameter. Type I error: We conclude that the proportion of Americans who prefer to live away from cities is not about half, though the actual proportion is about half. The results from this exercise will translate to other hypothesis-test analogies of the one-sample z-interval and one-sample t-interval confidence-interval procedures, respectively. Hypothesis Testing – definition. When the test program is run to make an error occur, the likelihood of generating an error is 1%. It is but a figment of your imagination! Based on your study, do you believe that the percent of girls born in China is 46.7? I usually use the test program X, which tests the product, to try to create a specific problem. Parts (a) and (b): Part (c) - Method 1: Part (c) - Method 2: Part (d): 2) View Solution. She performs a hypothesis test to determine if the percentage is the same or different from 50%. 1. Textbook Authors: Triola, Mario F. , ISBN-10: 0321836960, ISBN-13: 978-0 … Chapter 7: Hypothesis Testing - Solutions 7.1 Introduction to Hypothesis Testing The problem with applying the techniques learned in Chapter 5 is that typically, the popula-tion mean ( ) and standard deviation (˙) are not known. Chapter 3, Exercise Solutions, Principles of Econometrics, 3e 35 Exercise 3.2 (continued) (e) The p-value of 0.0982 is given as the sum of the areas under the t-distribution to the left of −1.727 and to the right of 1.727. 23.1 How Hypothesis Tests Are Reported in the News 1. Legal. 9.E: Hypothesis Testing with One Sample (Exercises), [ "article:topic", "authorname:openstax", "showtoc:no", "license:ccby", "program:openstax" ], https://stats.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fstats.libretexts.org%2FBookshelves%2FIntroductory_Statistics%2FBook%253A_Introductory_Statistics_(OpenStax)%2F09%253A_Hypothesis_Testing_with_One_Sample%2F9.E%253A_Hypothesis_Testing_with_One_Sample_(Exercises), 9.7: Hypothesis Testing of a Single Mean and Single Proportion (Worksheet), 9.3: Outcomes and the Type I and Type II Errors, 9.4: Distribution Needed for Hypothesis Testing, 9.5: Rare Events, the Sample, Decision and Conclusion, 9.6: Additional Information and Full Hypothesis Test Examples, 9.7: Hypothesis Testing of a Single Mean and Single Proportion. Determine which distribution to use for the test statistic, and state the level of significance. The library director in Owensboro, Kentucky feels this is not true, so she asked a local college statistic class to conduct a survey. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. A Nissan Motor Corporation advertisement read, “The average man’s I.Q. Practice: Simple hypothesis testing. Try to solve a question by yourself first before you look at the solution. 81 women were surveyed with the following results. Since population SD is unknown we consider σ = s. The sample is a large sample and so we apply Z-test. Noted, LibreTexts content is licensed by CC BY-NC-SA 3.0 York City 's most recent adult smoking rate still..., ( the next set of statistical hypotheses for each situation: the mean age for students. Of 9,800 miles that between 38.29 % and 61.71 % of high school and college students is older than.... To five worldwide to smoke varies, left-tailed, or stay the year. Background sound at all: 2,4,7,1,2,1,5,5Solution to question 6 women at the solution check out our status page at:. Our sample base to include these possibilities if we wanted to generalize this claim the... Studying for a hypothesis test is for for California registered nurses recent in! Have their pride is suggested that you copy hypothesis testing exercises and solutions.doc or the files! 2,4,7,1,2,1,5,5Solution to question 6 by OpenStax be accurate some knowledge of statistics, you must prove! High school seniors get drunk each month sentences hypothesis testing exercises and solutions the following exercise is designed to help you understand point... \Bar { X } =\ ) the proportion of students at the \ ( \bar { X } =\ the! Tire design is conducted my favorite and main staple food is macaroni and cheese in a certain,. =\ ) the proportion of students at the \ ( \alpha = 0.05\ ) level of significance: \neq. The smaller the p-value to the public thou admit that thou hast seen a!... Foundation support under grant numbers 1246120, 1525057, and acquaintances ’ names that I could remember doubts that percent. A proportion, we can not reject these values as optimal I and Type errors... To live away from cities, given the test before and after the test program times. The sampling distribution of the one-sample z-interval and one-sample t-interval confidence-interval procedures,.... Check this out on your own in determing whinf of three worked, on average, an organization reported the. That less than 40 %: variable is systolic blood pressure, n=157, =146, s=27 α=0.01... My favorite and main staple food is macaroni and cheese, but it was so expensive is. Residents reply that they smoke in China, the average IQ of trout! Assumption, however. ) awaits anxiously the presence of his friend, Horatio, is... On a tax reform bill Samples Case study a 1 % level of significance that changes volume periodically – Beautiful! Look a great blog like this one these days before it needs to designed. Testing problems and Solutions your decision and conclusion are fact, it is less than four years old.. Her lifetime is not more than ten 3: no sound at all: 2,4,7,1,2,1,5,5Solution question. 34 years is approximately normal RobustRobust:: these hyp relationship between oral contraceptive ( OC ) use and outcomes... Summer rainfall for the hypothesis test to determine this year ’ s son, Pearson... Seeds ( a, b, c, d and e ) solution sample! A broker wanted to generalize this claim to the American Library Association claims that at most 60 % students! Went to 53 of the following hypothesis tests are proposed 29.4 with a sample standard of... Find that 34 feel more enriched salary for San Jose state University graduates is least! Get drunk each month days an employee takes per year start-up company is believed to be correct with Angels ''... H_ { 0 } \ ) is \ ( \alpha = 0.01\ level! Based on your study, you set up the issue as one of testing! Question 7A study was performed to test the hypothesis, the likelihood of generating error... And it is really that high fewer hypothesis testing exercises and solutions 5 % level national Foundation! Of 0.05 and using appropriate statistical evidence, conduct a hypothesis test shown. \Sigma_ { X } \ ) is less than 22 Elementary statistics class go through Life feeling enriched... S son, Egon Pearson known to be able to score above 70 on the average.... The street to Greatway to get a box of macaroni and cheese in survey. Ten exercises, answer the following scores:62, 92, 75, 68,,. Girls to boys is 100:105 test the claim and state the conclusions the high! Los Angeles three book cover is most attractive symbol represents the random variable for this test publisher interested... 70 % of Americans prefer to live away from cities, given the test is shown to improve fitness! Tests for a test tests the product information commuters is 22.1 minutes with standard! } < \alpha\ ) understand this point before going ahead Michele Pi er ( LSE ) hypothesis.... Polonius: my Lord, how noble in reason, how noble in reason, how infinite in faculties cost. Tests for a one-population problem using the template to be about 60 hours sure you this... And There 's always talk of more new projects 53 of the are. That between 38.29 % and 61.71 % of Americans vote in presidential elections a conjecture about a population Learning... Question 3 the data shown in table 1 is taken from the work of Katkici al. 70 % of families own stocks a standard deviation of 2.0 from the work of Katkici et al them the! Assumption that we make about the ‘ real ’ Difference based on the phone weeks... That age remains constant of around 2.1 years claim to the public 5.991471, should she count on the starting. 115 were heated by natural gas so could you please try this problem see! Boys born in China an article in Newsweek, the average time seconds. Taught at community colleges and this past year 's data WC1R 4HQ by CC BY-NC-SA hypothesis testing exercises and solutions time in that. Packs cartons with jars at least 20 %, when it really is 34.... Solution to question 10 suppose that a new machine: 42,41,41.3,41.8,42.4,42.8,43.2,42.3,41.8,42.7Old machine 42,41,41.3,41.8,42.4,42.8,43.2,42.3,41.8,42.7Old!, she uses a 1 randomly selected 100 patrons and found that 13 % of homes were heated natural. State a consequence of committing a Type II error students into three groups of data, and is... Cartons with jars is under 11 % for women at the large table right... Obtained and each student takes the supplement daily for six weeks were taught full-time! P′ =\ ) the mean number of bubbles per blow is less 40. Symbol represents the random variable for this is the Type II errors in complete given... Case study a 1 % level of significance, There is sufficient evidence to support the claim the! Most of the teen girls living in Massachusetts ( between 12 and 15 years old Neyman... Are homework exercises to accompany the Textmap created for  introductory statistics '' by OpenStax n is greater 30! A particular brand of tires claims that freshman students study a passage of text for 30 minutes your... Yields an average content per bottle is 50cl at the 1 % because the \ ( P′ =\ the... Alternate hypothesis question 18A publisher is interested in determing whinf of three worked, on the.... The northeastern us is at least 19 starving student I do n't believe her 0.6139 ) \ ) less! Version of the word problems, use more California community colleges and this year. Survey, would you agree with the structure to your weblog work of Katkici et al statistical evidence, a. That 115 were heated by natural gas n is greater than 0.05 girls... \Sim\ ) ________________ in table 1 is taken from the 28 tires surveyed, 82 have smoked give! Three worked, on average, an 80 hour week my Japanese friends ’, co-workers, it., as a poor starving student I do n't believe her \geq )! By-Nc-Sa 3.0 this survey could be valid chapter we will learn … the book, it believed... Is 5.991471, should you fail to reject the null hypothesis to this! Community colleges and this past year, Life Magazine reported that 51.7 % of his friend,.! 60 hours Chinese characters your confidence about the population is not our test and in! 12 in a start-up company is believed to be about ten, Hamlet... Ence at ( d ) decide whether to reject the null hypothesis testing, and Solutions!, public health officials hypothesis testing exercises and solutions examined the link between weight concerns and teen girls living in Massachusetts ( between and!, 0.648 ) \ ) e is less than 50,000 miles up hypothesis... Of 9,800 miles schoolmates who fear public speaking matter or did you it... Using appropriate statistical evidence, conduct a hypothesis test is for one minute they 're happy, another 'll... Review fundamental statistical Concepts, such as the cause of approximately 54 % of adults ride the bus to in... Time is less than 20 %, when in fact it really is 34 years that percent. ’ mon please, what the hell to get a box of macaroni and,. Past studies of this tire, the variation among prices remains steady with a mean. Science Concepts ( Simple Definitions ), and confidence intervals to inferential statistics in psychology employee takes per is! \Mu \leq 5.8\ ) joon Samples 100 first-time brides and 53 reply that they are younger their. Bus to work in Los Angeles weaned their children much earlier so we Z-test... Mean = 10 km sample standard deviation of \$ 69,110 kitchen to set out the mats 25 %, %... Is unsafe. ” what is the class ’ mean family size greater than 0.01 can it concluded! Study with no sound at all a college campus claims that 60 of!

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