Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test. 1) A psychologist claims that more than 4.6 percent of the population suffers from professional problems due to extreme shyness. Identify the type II error for the test. A) The error of rejecting the claim that the true proportion is at most 4.6 percent when it really is at most 4.6 percent. B) The error of rejecting the claim that the true proportion is more than 4.6 percent when it really is more than 4.6 percent. C) The error of failing to reject the claim that the true proportion is at most 4.6 percent when it is actually more than 4.6 percent. Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis. 2) a = 0.09 for a right-tailed test. A) +1.645 B) +1.96 C) ±1.645 D) ±1.96 Determine whether the given conditions justify testing a claim about a population mean m. 3) The sample size is n = 21, s = 6.10, and the original population is normally distributed. A) No B) Yes Determine whether the given conditions justify using the margin of error E = z a/2 s/ interval estimate of the population mean m. 4) The sample size is n = 216 and s = 16. A) Yes B) No n when finding a confidence Determine whether the hypothesis test involves a sampling distribution of means that is a normal distribution, Student t distribution, or neither. 5) Claim: m = 118. Sample data: n = 17, x = 101, s = 15.4. The sample data appear to come from a normally distributed population with unknown m and s. A) Neither B) Student t C) Normal Do one of the following, as appropriate: (a) Find the critical value za/2, (b) find the critical value ta/2, (c) state that neither the normal nor the t distribution applies. 6) 98%; n = 7; s = 27; population appears to be normally distributed. A) za/2 = 2.33 B) ta/2 = 2.575 C) ta/2 = 1.96 D) za/2 = 2.05 7) 95%; n = 11; s is known; population appears to be very skewed. A) ta/2 = 2.228 B) za/2 = 1.812 C) za/2 = 1.96 D) Neither the normal nor the t distribution applies. 1
Express the confidence interval in the form of p^ ± E. 8) -0.052 < p < 0.568 A) p^ = 0.258 ± 0.5 B) p^ = 0.258 ± 0.31 C) p^ = 0.31 ± 0.5 D) p^ = 0.258-0.31 Find the P-value for the indicated hypothesis test. 9) An article in a journal reports that 34% of American fathers take no responsibility for child care. A researcher claims that the figure is higher for fathers in the town of Littleton. A random sample of 225 fathers from Littleton, yielded 97 who did not help with child care. Find the P-value for a test of the researcher's claim. A) 0.0529 B) 0.0015 C) 0.0019 D) 0.0038 Find the margin of error for the 95% confidence interval used to estimate the population proportion. 10) In a survey of 3000 T.V. viewers, 40% said they watch network news programs. A) 0.0131 B) 0.0230 C) 0.0201 D) 0.0175 Find the margin of error. _ 11) 95% confidence interval; n = 12; x = 46.4; s = 4.9 A) 3.736 B) 2.802 C) 2.335 D) 3.113 Find the minimum sample size you should use to assure that your estimate of p^ will be within the required margin of error around the population p. 12) Margin of error: 0.008; confidence level: 99%; from a prior study, p^ is estimated by 0.220 A) 16,001 B) 142 C) 10,301 D) 17,779 13) Margin of error: 0.003; confidence level: 93%; p^ and q^ are unknown A) 91,003 B) 274 C) 151 D) 91,002 Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. 14) A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the s = 3.3 mg claimed by the manufacturer. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms. A) There is sufficient evidence to support the claim that the standard deviation is equal to 3.3 mg. B) There is not sufficient evidence to support the claim that the standard deviation is different from 3.3 mg. C) There is not sufficient evidence to support the claim that the standard deviation is equal to 3.3 mg. D) There is sufficient evidence to support the claim that the standard deviation is different from 3.3 mg. 15) An entomologist writes an article in a scientific journal which claims that fewer than 14 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms. A) There is not sufficient evidence to support the claim that the true proportion is less than 14 in ten thousand. B) There is not sufficient evidence to support the claim that the true proportion is greater than 14 in ten thousand. C) There is sufficient evidence to support the claim that the true proportion is less than 14 in ten thousand. D) There is sufficient evidence to support the claim that the true proportion is greater than 14 in ten thousand. 2
Identify the null hypothesis H0 and the alternative hypothesis H1. Use m for a claim about a mean, p for a claim about a proportion, and s for a claim about variation. 16) The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, m, of 41eF, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect. A) H0: m 41e B) H0: m 41e C) H0: m 41e D) H0: m = 41e H1: m = 41e H1: m > 41e H1: m < 41e H1: m 41e 17) The owner of a football team claims that the average attendance at games is over 73,700, and he is therefore justified in moving the team to a city with a larger stadium. A) H0: m, the average attendance at games, is greater than 73,700 H1: m, the average attendance at games, is less than or equal to 73,700 B) H0: m, the average attendance at games, is less than 73,700 H1: m, the average attendance at games, is greater than or equal to 73,700 C) H0: m, the average attendance at games, is equal to 73,700 H1: m, the average attendance at games, is greater than 73,700 D) H0: m, the average attendance at games, is equal to 73,700 H1: m, the average attendance at games, is less than 73,700 Solve the problem. 18) 36 randomly picked people were asked if they rented or owned their own home, 10 said they rented. Obtain a point estimate of the true proportion of home owners. A) 0.217 B) 0.750 C) 0.722 D) 0.278 19) The following confidence interval is obtained for a population proportion, p: (0.333, 0.367) Use these confidence interval limits to find the margin of error, E. A) 0.017 B) 0.015 C) 0.018 D) 0.034 20) The following confidence interval is obtained for a population proportion, p: 0.556 < p < 0.584 Use these confidence interval limits to find the point estimate, p^. A) 0.564 B) 0.570 C) 0.556 D) 0.576 21) Find the value of z a/2 that corresponds to a level of confidence of 97.80 percent. A) 2 B) 29 C) -2 D) 0.011 Use the confidence level and sample data to find a confidence interval for estimating the population m. 22) A group of 62 randomly selected students have a mean score of 28.3 with a standard deviation of 3.4 on a placement test. What is the 90 percent confidence interval for the mean score, m, of all students taking the test? A) 27.3 < m < 29.3 B) 27.2 < m < 29.4 C) 27.6 < m < 29.0 D) 27.5 < m < 29.1 23) A random sample of 107 light bulbs had a mean life of x = 590 hours with a standard deviation of s = 27 hours. Construct a 90 percent confidence interval for the mean life, m, of all light bulbs of this type. A) 584 < m < 596 B) 583 < m < 597 C) 586 < m < 594 D) 585 < m < 595 3
Use the confidence level and sample data to find the margin of error E. 24) Systolic blood pressures for women aged 18-24: 94% confidence; n = 98, x = 114.2 mm Hg, s = 12.7 mm Hg A) 2.4 mm Hg B) 9.9 mm Hg C) 51.7 mm Hg D) 2.2 mm Hg Use the given degree of confidence and sample data to construct a confidence interval for the population mean m. Assume that the population has a normal distribution. 25) The football coach randomly selected ten players and timed how long each player took to perform a certain drill. The times (in minutes) were: 10.7 6.6 6.7 11.3 9.8 14.7 12.3 5.3 10.0 8.9 Determine a 95 percent confidence interval for the mean time for all players. A) 11.68 < m < 7.58 B) 7.68 < m < 11.58 C) 7.58 < m < 11.68 D) 11.58 < m < 7.68 26) The amounts (in ounces) of juice in eight randomly selected juice bottles are: 15.1 15.3 15.8 15.7 15.6 15.5 15.2 15.7 Construct a 98 percent confidence interval for the mean amount of juice in all such bottles. A) 15.80 < m < 15.17 B) 15.27 < m < 15.70 C) 15.70 < m < 15.27 D) 15.17 < m < 15.80 Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. 27) Of 82 adults selected randomly from one town, 66 have health insurance. Find a 90% confidence interval for the true proportion of all adults in the town who have health insurance. A) 0.719 < p < 0.891 B) 0.692 < p < 0.918 C) 0.703 < p < 0.907 D) 0.733 < p < 0.877 28) n = 105, x = 67; 88 percent A) 0.565 < p < 0.711 B) 0.564 < p < 0.712 C) 0.561 < p < 0.715 D) 0.560 < p < 0.716 Use the margin of error, confidence level, and standard deviation s to find the minimum sample size required to estimate an unknown population mean m. 29) Margin of error: $133, confidence level: 99%, s = $533 A) 54 B) 62 C) 107 D) 0 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic, P-value, critical value(s), and state the final conclusion. 30) Test the claim that the mean lifetime of car engines of a particular type is greater than 220,000 miles. Sample data are summarized as n = 23, x = 226,450 miles, and s = 11,500 miles. Use a significance level of a = 0.01. 4
Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. 31) Various temperature measurements are recorded at different times for a particular city. The mean of 25eC is obtained for 60 temperatures on 60 different days. Assuming that s = 1.5eC, test the claim that the population mean is 23eC. Use a 0.05 significance level. 32) In a clinical study of an allergy drug, 108 of the 202 subjects reported experiencing significant relief from their symptoms. At the 0.01 significance level, test the claim that more than half of all those using the drug experience relief. 33) A nationwide study of American homeowners revealed that 64% have one or more lawn mowers. A lawn equipment manufacturer, located in Omaha, feels the estimate is too low for households in Omaha. Can the value 0.64 be rejected if a survey of 490 homes in Omaha yields 331 with one or more lawn mowers? Use a = 0.05. Provide an appropriate response. 34) Interpret the following 95% confidence interval for mean weekly salaries of shift managers at Guiseppe's Pizza and Pasta. 325.80 < m < 472.30 35) Under what circumstances can you replace s with s in the formula E = z a/2 œ s n. 5
36) Describe the steps for finding a confidence interval. 37) Define Type I and Type II errors. Give an example of a Type I error which would have serious consequences. Give an example of a Type II error which would have serious consequences. What should be done to minimize the consequences of a serious Type I error? Test the given claim using the traditional method of hypothesis testing. Assume that the sample has been randomly selected from a population with a normal distribution. 38) A researcher wants to check the claim that convicted burglars spend an average of 18.7 months in jail. She takes a random sample of 11 such cases from court files and finds that x = 20.2 months and s = 8 months. Test the null hypothesis that m = 18.7 at the 0.05 significance level. 39) A public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes. Karen took bus number 14 during peak hours on 18 different occasions. Her mean waiting time was 7.8 minutes with a standard deviation of 2.5 minutes. At the 0.01 significance level, test the claim that the mean is less than 10 minutes. 6
Answer Key Testname: SAMPLETEST2.TST MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) C Page Ref: 381-385 2) A Page Ref: 374-375 3) B Page Ref: 400-403 4) A Page Ref: 320-321 5) B Page Ref: 408-414 6) A Page Ref: 330-339 7) D Page Ref: 330-339 8) B Page Ref: 301-304 9) C Page Ref: 391-392 10) D Page Ref: 305 11) D Page Ref: 334-339 12) D Page Ref: 308-309 13) A Page Ref: 307-308 14) B Page Ref: 376-381 15) C Page Ref: 376-381 16) D Page Ref: 373-374 17) C Page Ref: 373-374 18) C Page Ref: 310-311 19) A Page Ref: 301-304 20) B Page Ref: 301-304 21) A Page Ref: 301-304 1
Answer Key Testname: SAMPLETEST2.TST 22) C Page Ref: 320-324 23) C Page Ref: 320-324 24) A Page Ref: 322-324 25) C Page Ref: 330-339 26) B Page Ref: 330-339 27) D Page Ref: 306-307 28) A Page Ref: 306-307 29) C Page Ref: 324-326 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 30) a = 0.05 Test statistic: t = 2.69 t > 2.5080 Because t > 2.5080, we reject the null hypothesis. There is sufficient evidence to accept the claim that m > 220,000 miles. Page Ref: 408-414 31) H0: m = 23; H1: m > 23. Test statistic: z = 10.33;. P-value: 0.0002. Because the P-value of 0.0002 is less than the significance level of a = 0.05, we reject the null hypothesis. Page Ref: 400-403 32) H0: p = 0.5. H1: p > 0.5. Test statistic: z = 0.99. Critical values: z = 2.33. Fail to reject null hypotheis. There is not sufficient evidence to support the claim that more than half of all those using the drug experience relief. Page Ref: 389-391 33) H0: p = 0.65. H1: p > 0.65. Test statistic: z = 1.64. Critical value: z = 1.645. Fail to reject null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the proportion with lawn mowers in Omaha is 0.64. Page Ref: 389-391 34) We are 95% sure that the interval contains the true population value for mean weekly salaries of shift managers at Guiseppe's Pizza and Pasta. Page Ref: 298-355 35) Provided n > 30, s can be used in place of s. If n 30, the population must be normal and s must be known to use the formula. Page Ref: 298-355 36) Begin with the summary statistics for x and s. Determine whether the z or t distribution is required. Compute the error estimate using either E = z a/2 œ sn or E = t a/2 œ s. Find the interval using x ± E. Interpret the confidence interval. n Page Ref: 298-355 2
Answer Key Testname: SAMPLETEST2.TST 37) Type I: The mistake of rejecting the null hypothesis when it is true. Type II: The mistake of failing to reject the null hypothesis when it is false. Answers for examples will vary. To minimize a Type I error with serious consequences, make a smaller. Also, make the sample size larger to minimize both a and b. Page Ref: 368-423 38) Test statistic: t = 0.62. Critical values: t = ±2.228. Fail to reject H0. There is not sufficient evidence to warrant rejection of the claim that the mean is 18.7 months. Page Ref: 408-414 39) Test statistic: t = -3.73. Critical values: t = -2.567. Reject H0. There is sufficient evidence to support the claim that the mean is less than 10 minutes. Page Ref: 408-414 3