Chapter 7 - Practice Problems 2

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1 Chapter 7 - Practice Problems 2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the requested value. 1) A researcher for a car insurance company wishes to estimate the mean annual premium that men aged pay for their car insurance. A random sample of 16 men aged between 20 and 24 yields the following annual premiums, in dollars. 1) Use the data to obtain a point estimate of the mean annual premium for all men aged between 20 and 24. Round your answer to the nearest dollar. A) $727 B) $709 C) $718 D) $705 2) Is it true that the point estimate of a population mean must lie within the range of values defined by the corresponding confidence-interval estimate, regardless of the level of confidence achieved? Explain. A) Yes. By definition, the prescribed confidence interval contains the value of the point estimate. B) No. The confidence interval only defines a range of values that is likely to contain the point estimate with some prescribed level of confidence. This range of values is not guaranteed to contain the point estimate. 2) Solve the problem. 3) Find the level of confidence that corresponds to a value of α of ) A) 13% B) 0.065% C) 87% D) 0.87% 4) Find the value of α that corresponds to a level of confidence of 96%. 4) A) 0.04 B) C) 0.96 D) 4 Find the confidence interval specified. 5) The mean score, x, on an aptitude test for a random sample of 2 students was 73. Assuming that σ = 12, construct a 95.44% confidence interval for the mean score, μ, of all students taking the test. 5) A) 56.0 to 90.0 B) 60.3 to 85.7 C) 49 to 97 D) 61.0 to ) A sample of 45 people were randomly selected from among the workers in a shoe factory. The time taken for each person to polish a finished shoe was measured. The sample mean was 2.3 minutes. Assume that σ = 0.23 minutes. Construct a 90% confidence interval for the true mean time, μ, to polish a shoe. 6) A) 2.24 to 2.36 minutes B) 2.21 to 2.39 minutes C) 2.22 to 2.38 minutes D) 2.23 to 2.37 minutes 1

2 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 7) Mary wishes to estimate the mean height of women aged She picks a sample of 100 women aged between 18 and 24 and constructs a 99% confidence interval for the population mean. If she were to repeat this procedure 200 times in total, she would obtain 200 different confidence intervals. How many of these intervals would you expect to contain the population mean, μ? Explain your thinking. 7) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine the margin of error in estimating the population mean, μ. 8) A sample of 47 eggs yields a mean weight of 1.74 ounces. Assuming that σ = 0.29 ounces, find the margin of error in estimating μ at the 95% level of confidence. 8) A) 0.07 oz B) 0.08 oz C) 0.01 oz D) 6.86 oz 9) A sample of 74 college students yields a mean annual income of $3494. Assuming that σ = $844, find the margin of error in estimating μ at the 99% level of confidence. 9) A) $229 B) $9 C) $253 D) $1046 Find the specified t-value. 10) For a t-curve with df = 11, find t ) A) B) C) D) ) For a t-curve with df = 20, find t ) A) B) C) D) ) For a t-curve with df = 9, find the t-value having area to its left. 12) A) B) C) D) Find the confidence interval specified. Assume that the population is normally distributed. 13) A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 199 milligrams with s = 16.5 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs. 13) A) to milligrams B) to milligrams C) to milligrams D) to milligrams 14) Thirty randomly selected students took the calculus final. If the sample mean was 88 and the standard deviation was 7.1, construct a 99% confidence interval for the mean score of all students. 14) A) to B) to C) to D) to

3 15) The amounts (in ounces) of juice in eight randomly selected juice bottles are: 15) Construct a 98% confidence interval for the mean amount of juice in all such bottles. A) to ounces B) to ounces C) to ounces D) to ounces 16) The data below consists of the test scores from a sample of 32 students. Construct a 95.44% confidence interval for the population mean score of all students. 16) A) to B) to C) to D) to ) Suppose that you wish to obtain a confidence interval for a population mean. Under the conditions described below, should you use the z-interval procedure, the t-interval procedure, or neither? 17) - The population standard deviation is known. - The population is not normally distributed. - The sample size is 12. A) z-interval procedure B) t-interval procedure C) Neither Find the indicated margin of error. 18) In a sample of 198 observations, there were 80 positive outcomes. Find the margin of error for the 95% confidence interval used to estimate the population proportion. 18) A) B) C) D) ) In a survey of 2300 T.V. viewers, 690 said they watch network news programs. Find the margin of error for the 95% confidence interval used to estimate the population proportion. 19) A) B) C) D) Find the indicated confidence interval. 20) A researcher wishes to estimate the proportion of adults in the city of Darby who are vegetarian. In a random sample of 1624 adults from this city, the proportion that are vegetarian is Find a 90% confidence interval for the true proportion of vegetarians in the city of Darby. 20) A) From to B) From to C) From to D) From to

4 21) In a sample of 1788 patients who underwent a certain type of surgery, 15% experienced complications. Find a 99% confidence interval for the proportion of all those undergoing this surgery who experience complications. 21) A) From to B) From to C) From to D) From to ) A study involves 635 randomly selected deaths, with 29 of them caused by accidents. Construct a 98% confidence interval for the true percentage of all deaths that are caused by accidents. 22) A) From 3.20% to 5.93% B) From 2.94% to 6.19% C) From 2.43% to 6.70% D) From 2.64% to 6.50% Assume that you wish to estimate a population proportion, p. For the given margin of error and confidence level, determine the sample size required. 23) You wish to estimate the proportion of all voters in California who plan to vote in favor of a 23) certain ballot measure. Obtain a sample size that will ensure a margin of error of at most 0.01 for a 99% confidence interval. Assume that it is reasonable to presume that of the voters sampled, the percentage in favor of the measure will be between 15% and 26%. A) 16,577 B) 8455 C) 12,758 D) ) You wish to estimate the proportion of shoppers that use credit cards. Determine the sample size needed. It is deemed reasonable to presume that of those samples, the percentage using credit cards will be at least 66%. The margin of error should be at most The confidence level is 95%. 24) A) 485 B) 1585 C) 930 D) 539 Find the required sample size without making a guess for the observed value of p^. 25) A pollster wishes to estimate the true proportion of U.S. voters that oppose capital punishment. How many voters should be surveyed in order to be 94 percent confident that the true proportion is estimated to within 0.08? 25) A) 12 B) 139 C) 138 D) 1 26) A researcher wishes to estimate the proportion of fish in a certain lake that is inedible due to pollution of the lake. How large a sample should be tested in order to be 97 percent confident that the true proportion of inedible fish is estimated to within 0.06? 26) A) 151 B) 327 C) 10 D) ) Suppose that you wish to estimate a population proportion and want to determine a sample size that will ensure a given margin of error for a 95% confidence interval. Suppose further that an educated guess of 0.3 is used for p^ when determining the sample size. What values of the observed value of p^ will yield a larger margin of error than the one specified? 27) A) 0.3 < p^ < 0.5 B) p^ > 0.3 C) p^ < 0.3 D) 0.3 < p^ < 0.7 4

5 28) Suppose that the proportion of left handers in a certain population is 10%. Let p^ represent the proportion of left handers in a random sample from this population. Which of the following describes the distribution of p^ for samples of size 100? 28) A: Approximately normal with a mean of 0.1 and a standard deviation of 0.03 B: Exactly normal with a mean of 0.1 and a standard deviation of 0.03 C: Approximately normal with a mean of 0.1 and a standard deviation of D: Exactly normal with a mean of 0.1 and a standard deviation of A) A B) D C) C D) B 29) You are planning to use a sample proportion p^ to estimate a population proportion, p. A sample size of 100 and a confidence level of 95% yielded a margin of error of Which of the following will result in a larger margin of error? A: Increasing the sample size while keeping the same confidence level B: Decreasing the sample size while keeping the same confidence level C: Increasing the confidence level while keeping the same sample size D: Decreasing the confidence level while keeping the same sample size 29) A) A and D B) B and C C) A and C D) B and D 30) The college daily reported: ʺ450 students living in university housing were polled. 270 said that they were satisfied with their living conditions. Based on this survey we conclude that 60% of students living in dormitories are satisfied. The margin of error of the study is ± 5 percentage points (with a 95% degree of confidence). Which statement is correct? 30) A) The margin of error is consistent with the sample size. B) The stated margin of error could have been achieved with a smaller sample size. C) A larger sample should be used to achieve the stated margin of error. D) There is not enough information to determine whether the margin of error is consistent with the sample size. 5

6 Answer Key Testname: CH 7 SET 2 1) A 2) A 3) C 4) A 5) A 6) A 7) Approximately 198 of the intervals will contain the population mean. The chance that any given confidence interval contains the true mean is 99%, so out of 200 such confidence intervals approximately 99% of 200, or 198, intervals will contain μ. 8) B 9) C 10) C 11) C 12) C 13) C 14) C 15) B 16) C 17) C 18) C 19) A 20) B 21) B 22) D 23) C 24) D 25) B 26) D 27) D 28) A 29) B 30) B 6

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