Testing Claims about Variation. In

Waiting in Line The Jefferson Valley Bank once had a separate customer waiting line at each teller window, but it now has a single waiting line that feeds the teller windows as vacancies occur. The standard deviation of customer waiting times with the old multiple-­line configuration was 1.8 min. Listed below is a simple random sample of waiting times (minutes) with the single waiting line. The 10 sample values have a standard deviation of 0.5 min. a. When the bank changed from multiple waiting lines to a single line, how was the mean waiting time affected? 6.5 6.6 6.7 6.8 7.1 7.3 7.4 7.7 7.7 7.7 b. When the bank changed from multiple waiting lines to a single line, how was the variation among waiting times affected? c. What improvement occurred with the change from multiple waiting lines to a single line? d. What procedure can be used to determine that the single waiting line is better?

Large Data Sets from Appendix B. In Exercises 17 and 18, use the data set from Appendix B to test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P­-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Weights of Pennies Data Set 21 in Appendix B includes a simple random sample of “wheat” pennies. U.S. Mint specifications now use a standard deviation of 0.0230 g for weights of pennies. Use a 0.01 significance level to test the claim that wheat pennies were manufactured so that their weights have a standard deviation equal to 0.0230 g.

Problem 1RE True/False Characterize each of the following statements as being true or false. a. In a hypothesis test, a very high P-value indicates strong support of the alternative hypothesis. ________________ b. The Student t distribution can be used to test a claim about a population mean whenever the sample data are randomly selected from a normally distributed population. ________________ c. When using a ?2 distribution to test a claim about a population standard deviation, there is a very loose requirement that the sample data be from a population having a normal distribution. ________________ d. When conducting a hypothesis test about the claimed proportion of adults who have current passports, the problems with a convenience sample can be overcome by using a larger sample size. ________________ e. When repeating the same hypothesis test with different random samples of the same size, the conclusions will all be the same.

Requirements If we want to use the sample data from Exercise 1 to test the claim that the sample is from a population with a standard deviation less than 1.8 min, we must satisfy the requirements of having a simple random sample and a normally distributed population. In Exercise 1 it was stated that the sample is a simple random sample. a. In general, how does the normality requirement for a hypothesis test of a claim about a standard deviation differ from the normality requirement for a hypothesis test of a claim about a mean? b. What methods can be used to determine whether the normality requirement is satisfied?

Type of Test Refer to the hypothesis test described in Exercise 1. a. Is the hypothesis test left­-tailed, right­-tailed, or two­-tailed? b. If the requirements are satisfied, what distribution should be used for the hypothesis test: normal, Student t, chi­-square, binomial?

Problem 1CRE Dictionary Words A simple random sample of pages from Merriam-Webster’s Collegiate Dictionary, 11th edition, is obtained. Listed below are the numbers of words defined on those pages. Find the values of the indicated statistics. 51 63 36 43 34 62 73 39 53 79 a. Mean b. Median c. Standard deviation d. Variance e. Range

Wristwatch Accuracy Students of the author collected a simple random sample of times (sec) of wristwatch errors, and a few of those times are listed below. Negative values correspond to watches that are running ahead of the actual time. Assuming that we want to use a 0.05 significance level to test the claim that the sample is from a population with a mean equal to 0 sec, identify the null hypothesis and the alternative hypothesis. 140 ? 85 325 20 305 205 20 ? 93

Problem 2RE Leisure Time In a Gallup poll, 1010 adults were randomly selected and asked if they were satisfied or dissatisfied with the amount of leisure time that they had. Of this sample 657 said that they were satisfied and 353 said that they were dissatisfied. Use a 0.01 significance level to test the claim that 2/3 of adults are satisfied with the amount of leisure time that they have.

Confidence Interval Method of Hypothesis Testing Assume that we want to use the sample data from Exercise 1 to test the claim that the sample is from a population with a standard deviation less than 1.8 min? we will use a 0.05 significance level to test that claim. If we want to use the confidence interval method of testing hypotheses, what level of confidence should be used for the confidence interval? Will the conclusion based on the confidence interval be the same as the conclusion based on a hypothesis test that uses the P-­value method or the critical value method?

P-­Value If we use technology to conduct the hypothesis test described in Exercise 1, we get a P-­value of 0.1150. a. What should we conclude about the null hypothesis? b. What is the final conclusion that addresses the original claim?

Problem 3CRE Confidence Interval for Dictionary Words Use the sample values given in Exercise to construct a 95% confidence interval estimate of the population mean. Assume that the population has a normal distribution. Exercise Dictionary Words A simple random sample of pages from Merriam-Webster’s Collegiate Dictionary, 11th edition, is obtained. Listed below are the numbers of words defined on tt pages. Find the values of the indicated statistics. a. Mean b. Median c. Standard deviation d. Variance e. Range

Hypothesis Test For the sample data from Exercise 1, we have s = 0.5 and we want to use that sample to test the claim that the sample is from a population with a standard deviation less than 1.8 min (as it was in the past with multiple waiting lines). a. Identify the null and alternative hypotheses. b. Find the value of the test statistic. c. Using technology, the P-­value is found to be 0.0001. What should we conclude about the null hypothesis? d. Given that the P-­value is 0.0001, what should we conclude about the original claim? e. What does the conclusion suggest about the effectiveness of the change from multiple waiting lines to a single line?

Problem 2CRE Dictionary Words Refer to the sample data in Exercise. a. What is the level of measurement of the data (nominal, ordinal, interval, ratio)? ________________ b. Are the values discrete or continuous? ________________ c. What does it mean to state that the sample is a simple random sample? Exercise Dictionary Words A simple random sample of pages from Merriam-Webster’s Collegiate Dictionary, 11th edition, is obtained. Listed below are the numbers of words defined on tt pages. Find the values of the indicated statistics. 51 63 36 43 34 62 73 39 53 79 a. Mean b. Median c. Standard deviation d. Variance e. Range

Problem 3RE Risky Behavior In a USA Today poll of 737 respondents, 92% said that they do not open unfamiliar e-mail and instant-message links. Use a 0.01 significance level to test the claim that more than 75% of us do not open unfamiliar e-mail and instant-message links. How is the validity of the results affected by the knowledge that USA Today posted a question on its Web site, and 737 people chose to respond?

Normality For the hypothesis test in Exercise 1, what does it mean when we say that the test is robust against departures from normality?

Problem 4CRE Hypothesis Test for Dictionary Words Refer to the sample data given in Exercise. Given that the dictionary has 1459 pages with defined words, the claim that there are more than 70, 000 defined words is the same as the claim that the mean number of defined words on a page is greater than 48.0. Use a 0.05 significance level to test the claim that the mean number of defined words on a page is greater than 48.0. What does the result suggest about the claim that there are more than 70, 000 defined words in the dictionary? Exercise Dictionary Words A simple random sample of pages from Merriam-Webster’s Collegiate Dictionary, 11th edition, is obtained. Listed below are the numbers of words defined on tt pages. Find the values of the indicated statistics. a. Mean b. Median c. Standard deviation d. Variance e. Range

Problem 4RE Birth Weight A simple random sample of 1862 births of Chinese babies resulted in a mean birth weight of 3171 g and a standard deviation of 428 g (based on “Comparison of Birth Weight Distributions between Chinese and Caucasian Infants, ” by Wen et al., American Journal of Epidemiology, Vol. 172, No 10). Use a 0.01 significance level to test the claim that the mean birth weight of Chinese babies is less than the mean birth weight of 3369 g for Caucasian babies.

Testing Claims About Variation. In Exercises 5–16, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P­-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Assume that a simple random sample is selected from a normally distributed population. Cans of Coke Data Set 19 in Appendix B includes volumes (oz) of a simple random sample of 36 cans of regular Coke. Those volumes have a mean of 12.19 oz and a standard deviation of 0.11 oz, and they appear to be from a normally distributed population. If we want the filling process to work so that almost all cans have volumes between 11.8 oz and 12.4 oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.15 oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.15 oz. Use a 0.05 significance level.

Problem 5RE Birth Weights A simple random sample of 81 births of Chinese babies resulted in a mean birth weight of 3245 g and a standard deviation of 466 g. Test the claim that the standard deviation of birth weights of Chinese babies is equal to 567 g, which is the standard deviation of birth weights of Caucasian babies. Use a 0.01 significance level and assume that the birth weights are normally distributed.

Testing Claims About Variation. In Exercises 5–16, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P­-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Assume that a simple random sample is selected from a normally distributed population. Cans of Pepsi Repeat the preceding exercise using these statistics from a simple random sample of cans of regular Pepsi: \(n=36, x^{-}=12.29 \mathrm{oz}, s=0.09 \mathrm{oz}\) Equation Transcription: Text Transcription: n=36, x-=12.29 oz, s=0.09 oz

Problem 5CQQ Death Penalty Poll In a recent Gallup poll of 511 adults, 64% said that they were in favor of the death penalty for a person convicted of murder. We want to use a 0.01 significance level to test the claim that the majority of adults are in favor of the death penalty for a person convicted of murder. a. Identify the null and alternative hypotheses. ________________ b. Find the value of the test statistic. ________________ c. Technology is used to find this P-value: 1.263996E?10. Express the P-value in ordinary notation, then determine what we should conclude about the original claim.

P-Value Find the P­value in a test of the claim that the mean IQ score of acupuncturists is equal to 100, given that the test statistic is \(z\) = ? 2.00

Problem 5CRE Designing Cars The sitting height (from seat to top of head) of drivers must be considered in the design of a new car model. Men have sitting heights that are normally distributed with a mean of 36.0 in. and a standard deviation of 1.4 in. (based on anthropométrie survey data from Gordon, Churchill, et al.). a. One car is designed to accommodate sitting heights of 38.8 in. or less. Find the percentage of men with sitting heights greater than 38.8 in. ________________ b. If the sitting height is to be changed so that 98% of men will be accommodated, what is the new sitting height? ________________ c. If a car is occupied by four men, find the probability that they have a mean sitting height less than 37.0 in.

Problem 6CRE Left-Handedness Among Americans, 9.7% of males are left-handed and 12.5% of females are left-handed. a. If three females are randomly selected, find the probability that they are all left-handed. When randomly selecting three females, is it unlikely that all of them are left-handed? Why or why not? ________________ b. If one male is randomly selected and one female is randomly selected, find the probability that they are both left-handed. ________________ c. If five females are randomly selected, find the probability that at least one of them is left-handed.

Monitoring Lead in Air Listed below are measured amounts of lead (in micrograms per cubic meter, or \(\mu g / m 3\) , in the air. The Environmental Protection Agency has established an air quality standard for lead of \(1.5 \mu g / m 3\) . The measurements shown below constitute a simple random sample of measurements recorded at Building 5 of the World Trade Center site on different days immediately following the destruction caused by the terrorist attacks of September 11, 2001. After the collapse of the two World Trade Center buildings, there was considerable concern about the quality of the air. Use a 0.05 significance level to test the claim that the sample is from a population with a mean greater than the EPA standard of \(1.51 .5 \mu \mathrm{g} / \mathrm{m} 3\) . 5.40 1.10 0.42 0.73 0.48 1.10 Equation Transcription: Text Transcription: \mu g/m 3 1.5 \mu g/m 3 1.5 1.5 \mu g/m 3

Problem 7CQQ Equivalent Methods Which of the following statements are true? a. When testing a claim about ?, the P-value method, critical value method, and confidence interval method are all equivalent. ________________ b. When testing a claim about a population proportion p, the P-value method, critical value method, and confidence interval method are all equivalent. ________________ c. When testing a claim about any population parameter, the P-value method, critical value method, and confidence interval method are all equivalent.

Problem 7RE Pennsylvania Lottery In the Pennsylvania Match 6 lottery, six numbers between 1 and 49 are randomly drawn. To simulate the number selection process, a TI-83/84 Plus calculator was used to randomly generate 100 numbers between 1 and 49 inclusive. The sample has a mean of 24.2 and a standard deviation of 14.1. Use a 0.01 significance level to test the claim that the sample is selected from a population with a mean equal to 25, which is the mean of the population of all drawn numbers.

Normal Rainfall The following histogram is obtained from the daily rainfall amounts (in.) in Boston for a year. If we want to conduct a hypothesis test of a claim about the mean, there is a requirement that the population of rainfall amounts must have a normal distribution. Based on the histogram, does it appear that the population satisfies the requirement of a normal distribution? Why or why not?

Problem 8CQQ Chi-Square Test In a test of the claim that ? = 15 for the population of IQ scores of Facebook friends, we find the the rightmost critical value is ?2 = 71.420. Is the leftmost critical ?2 value equal to ?71.420?

Testing Claims About Variation. In Exercises 5–16, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P­-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Assume that a simple random sample is selected from a normally distributed population. Weights of Pennies The preceding exercise involved the claim that post­-1983 pennies have weights with a standard deviation less than 0.0230 g. Data Set 21 in Appendix B includes the weights of a simple random sample of 35 pre-­1983 pennies, and that sample has a standard deviation of 0.03910 g. Use a 0.05 significance level to test the claim that pre­-1983 pennies have weights with a standard deviation greater than 0.0230 g. Does it appear that weights of pre­-1983 pennies vary more than those of post­-1983 pennies?

Analyzing Graph The accompanying graph depicts results from a recent year in which there were 8878 male graduates and 8203 female graduates from medical schools in the United States. Does the graph depict the data in a way that is fair and objective, or is it somehow deceptive? Explain.

Testing Claims About Variation. In Exercises 5–16, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P­-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Assume that a simple random sample is selected from a normally distributed population. Weights of Pennies Data Set 21 in Appendix B includes a simple random sample of 37 weights of post­-1983 pennies. Those 37 weights have a mean of 2.49910 g and a standard deviation of 0.01648 g. U.S. Mint specifications require that pennies be manufactured so that the mean weight is 2.500 g. A hypothesis test will verify that the sample appears to come from a population with a mean of 2.500 g as required, but use a 0.05 significance level to test the claim that the population of weights has a standard deviation less than the specification of 0.0230 g.

Problem 8RE Type I Error and Type II Error a. In general, what is a type I error? In general, what is a type II error? ________________ b. For the hypothesis test in Exercise, write a statement that would constitute a type I error, and write another statement that would be a type II error. Exercise Pennsylvania Lottery In the Pennsylvania Match 6 lottery, six numbers between 1 and 49 are randomly drawn. To simulate the number selection process, a TI-83/84 Plus calculator was used to randomly generate 100 numbers between 1 and 49 inclusive. The sample has a mean of 24.2 and a standard deviation of 14.1. Use a 0.01 significance level to test the claim that the sample is selected from a population with a mean equal to 25, which is the mean of the population of all drawn numbers.

Problem 9CRE Gun Survey In a recent Gallup poll, 1003 randomly selected adults in the United States were asked if they have a gun in their home, and 37.2% of them answered “yes.” a. What is the number of respondents who answered “yes”? ________________ b. Construct a 95% confidence interval estimate of the percentage of all adults who would answer “yes” when asked if they have a gun in their home. ________________ c. Based on a hypothesis test, can we safely conclude that less than 50% of adults answer “yes” when asked if they have a gun in their home? Why or why not? ________________ d. What is a sensible response to the criticism that the Gallup poll cannot provide good results because the sample size is only 1003 adults selected from a large population of 241, 472, 385 adults in the United States?

Problem 9RE Pennsylvania Lottery and ?2 Test Assume that we want to use the same sample data from Exercise to test the claim that the standard deviation of all drawn numbers is less than 15.0. Why can’t we use a ?2 test with the methods described in Section 8-4? Exercise Pennsylvania Lottery In the Pennsylvania Match 6 lottery, six numbers between 1 and 49 are randomly drawn. To simulate the number selection process, a TI-83/84 Plus calculator was used to randomly generate 100 numbers between 1 and 49 inclusive. The sample has a mean of 24.2 and a standard deviation of 14.1. Use a 0.01 significance level to test the claim that the sample is selected from a population with a mean equal to 25, which is the mean of the population of all drawn numbers.

Testing Claims About Variation. In Exercises 5–16, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P­-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Assume that a simple random sample is selected from a normally distributed population. Pulse Rates of Men A simple random sample of 40 men results in a standard deviation of 10.3 beats per minute (based on Data Set 1 in Appendix B). The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.05 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute.

Problem 9CQQ Conclusions True or false: In hypothesis testing, it is never valid to form a conclusion of supporting the null hypothesis.

Problem 10CQQ Reliability True or false: If correct methods of hypothesis testing are used with a large simple random sample, the conclusion will always be true.

Testing Claims About Variation. In Exercises 5–16, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P­-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Assume that a simple random sample is selected from a normally distributed population. Pulse Rates of Women Repeat the preceding exercise using the pulse rates of women listed in Data Set 1 of Appendix B. For this sample, n = 40 and s = 11.6 beats per minute. ________________ Equation Transcription: Text Transcription: n=40 s=11.6

Problem 10CRE Hypothesis Test for Gun Survey Refer to the survey results from Exercise and use a 0.01 significance level to test the claim that fewer than 50% of Americans say that they have a gun in their home. Exercise Gun Survey In a recent Gallup poll, 1003 randomly selected adults in the United States were asked if they have a gun in their home, and 37.2% of them answered “yes.” a. What is the number of respondents who answered “yes”? ________________ b. Construct a 95% confidence interval estimate of the percentage of all adults who would answer “yes” when asked if they have a gun in their home. ________________ c. Based on a hypothesis test, can we safely conclude that less than 50% of adults answer “yes” when asked if they have a gun in their home? Why or why not? ________________ d. What is a sensible response to the criticism that the Gallup poll cannot provide good results because the sample size is only 1003 adults selected from a large population of 241, 472, 385 adults in the United States?

Problem 10RE Tests of Child Booster Seats The National Highway Traffic Safety Administration conducted crash tests of child booster seats for cars. Listed below are results from those tests, with the measurements given in HIC (standard head injury condition units). The safety requirement is that the HIC measurement should be less than 1000 HIC. Use a 0.01 significance level to test the claim that the sample is from a population with a mean less than 1000 HIC. Do the results suggest that all of the child booster seats meet the specified requirement? 602 696 762 572 637

Testing Claims About Variation. In Exercises 5–16, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P­-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Assume that a simple random sample is selected from a normally distributed population. Cigarette Tar A simple random sample of 25 filtered 100-­mm cigarettes is obtained, and the tar content of each cigarette is measured. The sample has a standard deviation of 3.7 mg (based on Data Set 10 in Appendix B). Use a 0.05 significance level to test the claim that the tar content of filtered 100­-mm cigarettes has a standard deviation different from 3.2 mg, which is the standard deviation for unfiltered king­-size cigarettes.

Problem 12BSC Testing Claims about Variation. In Exercises, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Assume that a simp L• random samp h is selected from a normally distributed population. Analysis of Pennies In an analysis investigating the usefulness of pennies, the cents portions of 100 randomly selected credit card charges from the author are recorded, and they have a mean of 47.6 cents and a standard deviation of 33.5 cents. If the amounts from 0 cents to 99 cents are all equally likely, the mean is expected to be 49.5 cents and the population standard deviation is expected to be 28.866 cents. Use a 0.01 significance level to test the claim that the sample is from a population with a standard deviation equal to 28.866 cents. If the amounts from 0 cents to 99 cents are all equally likely, is the requirement of a normal distribution satisfied? If not, how does that affect the conclusion?

Testing Claims About Variation. In Exercises 5–16, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P­-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Assume that a simple random sample is selected from a normally distributed population. Ages of Race Car Drivers Listed below are the ages (years) of randomly selected race car drivers (based on data reported in USA Today). Most people in the general population have ages that vary between 0 and 90 years, so use of the range rule of thumb suggests that ages in the general population have a standard deviation of 22.5 years. Use a 0.01 significance level to test the claim that the standard deviation of ages of all race car drivers is less than 22.5 years. 32 32 33 33 41 29 38 32 33 23 27 45 52 29 25

Testing Claims About Variation. In Exercises 5–16, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P­-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Assume that a simple random sample is selected from a normally distributed population. Highway Speeds Listed below are speeds (mi/h) measured from southbound traffic on I­-280 near Cupertino, California (based on data from SigAlert). This simple random sample was obtained at 3:30 p.m. on a weekday. Use a 0.05 significance level to test the claim of the highway engineer that the standard deviation of speeds is equal to 5.0 mi/h. 62 61 61 57 61 54 59 58 59 69 60 67

Testing Claims About Variation. In Exercises 5–16, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P­-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Assume that a simple random sample is selected from a normally distributed population. IQ of Professional Pilots The Wechsler IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Listed below are IQ scores of randomly selected professional pilots. It is claimed that because professional pilots are a more homogeneous group than the general population, they have IQ scores with a standard deviation less than 15. Test that claim using a 0.05 significance level. 121 116 115 121 116 107 127 98 116 101 130 114

Large Data Sets from Appendix B. In Exercises 17 and 18, use the data set from Appendix B to test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-­value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Cans of Diet Coke Repeat Exercise 5 using the volumes (oz) of cans of diet Coke.

Testing Claims About Variation. In Exercises 5–16, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P­-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Assume that a simple random sample is selected from a normally distributed population. Aircraft Altimeters The Skytek Avionics company uses a new production method to manufacture aircraft altimeters. A simple random sample of new altimeters resulted in the errors listed below. Use a 0.05 level of significance to test the claim that the new production method has errors with a standard deviation greater than 32.2 ft, which was the standard deviation for the old production method. If it appears that the standard deviation is greater, does the new production method appear to be better or worse than the old method? Should the company take any action? ? 42 78 ? 22 ? 72 ? 45 15 17 51 ? 5 ? 53 ? 9 ? 109

Problem 19BB Finding Critical Values of ? 2 For large numbers of degrees of freedom, we can approximate critical values of ?2 as follows: Here k is the number of degrees of freedom and z is the critical value(s) found from technology or Table A-2. In Exercise we have df = 35, so Table A-4 does not list an exact critical value. If we want to approximate a critical value of ?2 in the left-tailed hypothesis test with a = 0.05 and a sample size of 36, we let k = 35 with z = ? 1.645. Use this approximation to estimate the critical value of ?2 for Exercise. How close is it to the value of ?2 = 22.465 obtained by using STATDISK and Minitab? Exercise Testing Claims about Variation. In Exercises, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Assume that a simpL• random samph is selected from a normally distributed population. Cans of Coke Data Set 19 in Appendix B includes volumes (oz) of a simple random sample of 36 cans of regular Coke. Those volumes have a mean of 12.19 oz and a standard deviation of 0.11 oz, and they appear to be from a normally distributed population. If we want the filling process to work so that almost all cans have volumes between 11.8 oz and 12.4 oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.15 oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.15 oz. Use a 0.05 significance level.

Problem 20BB Finding Critical Values of ? 2 Repeat Exercise 1 using this approximation (with k and z as described in Exercise 1): Exercise 1 Finding Critical Values of ? 2 For large numbers of degrees of freedom, we can approximate critical values of ?2 as follows: Here k is the number of degrees of freedom and z is the critical value(s) found from technology or Table A-2. In Exercise 2 we have df = 35, so Table A-4 does not list an exact critical value. If we want to approximate a critical value of ?2 in the left-tailed hypothesis test with a = 0.05 and a sample size of 36, we let k = 35 with z = ? 1.645. Use this approximation to estimate the critical value of ?2 for Exercise. How close is it to the value of ?2 = 22.465 obtained by using STATDISK and Minitab? Exercise 2 Testing Claims about Variation. In Exercises, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Assume that a simpL• random samph is selected from a normally distributed population. Cans of Coke Data Set 19 in Appendix B includes volumes (oz) of a simple random sample of 36 cans of regular Coke. Those volumes have a mean of 12.19 oz and a standard deviation of 0.11 oz, and they appear to be from a normally distributed population. If we want the filling process to work so that almost all cans have volumes between 11.8 oz and 12.4 oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.15 oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.15 oz. Use a 0.05 significance level.