Chapter 7 - Practice Problems 1

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1 Chapter 7 - Practice Problems 1 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) Define a point estimate. What is the best point estimate for µ? 1) 2) Define margin of error. Explain the relation between the confidence interval and the error estimate. Suppose a confidence interval is 9.65 < µ < Find the sample mean x and the error estimate E. 2) 3) How do you determine whether to use the z or t distribution in computing the margin of error, E = z /2 n or E = t /2 s n? 3) 4) When determining the sample size needed to achieve a particular error estimate you need to know. What are two methods of estimating if is unknown? 4) 5) Interpret the following 95% confidence interval for mean weekly salaries of shift managers at Guiseppe's Pizza and Pasta < µ < ) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 6) Find the critical value z /2 that corresponds to a degree of confidence of 98%. 6) A) B) 2.05 C) 2.33 D) ) Find the critical value z /2 that corresponds to a degree of confidence of 91%. 7) A) 1.75 B) 1.70 C) D) 1.34 ^ Express the confidence interval in the form of p ± E. 8) < p < ) A) ^p = B) ^p = 0.4 ± 0.5 C) ^p = ± 0.5 D) ^p = ± 0.4 1

2 Solve the problem. 9) The following confidence interval is obtained for a population proportion, p: (0.700, 0.728) ^ Use these confidence interval limits to find the point estimate, p. 9) A) B) C) D) ) The following confidence interval is obtained for a population proportion, p: < p < Use these confidence interval limits to find the margin of error, E. 10) A) B) C) D) Find the margin of error for the 95% confidence interval used to estimate the population proportion. 11) n = 151, x = ) A) B) C) D) ) In a survey of 4800 T.V. viewers, 50% said they watch network news programs. 12) A) B) C) D) Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. 13) n = 54, x = 13; 95 percent 13) A) < p < B) < p < C) < p < D) < p < ) n = 140, x = 81; 90 percent 14) A) < p < B) < p < C) < p < D) < p < ^ 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. 15) Margin of error: 0.012; confidence level: 93%; p and q unknown 15) A) 5700 B) 1 C) 38 D) ) Margin of error: 0.006; confidence level: 97%; p and q unknown 16) A) 197 B) 32,704 C) 196 D) 32,702 17) Margin of error: 0.07; confidence level: 90%; from a prior study, p is estimated by ) A) 285 B) 84 C) 7 D) 95 18) Margin of error: 0.03; confidence level: 95%; from a prior study, p is estimated by the decimal equivalent of 58%. A) 1040 B) 1795 C) 936 D) ) 2

3 Solve the problem. 19) Find the point estimate of the true proportion of people who wear hearing aids if, in a random sample of 496 people, 73 people had hearing aids. 19) A) B) C) D) ) 50 people are selected randomly from a certain population and it is found that 13 people in the sample are over 6 feet tall. What is the point estimate of the true proportion of people in the population who are over 6 feet tall? 20) A) 0.50 B) 0.74 C) 0.26 D) 0.19 Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. 21) A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature. Construct the 95% confidence interval for the true proportion of all voters in the state who favor approval. 21) A) < p < B) < p < C) < p < D) < p < Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. 22) Of 99 adults selected randomly from one town, 63 have health insurance. Find a 90% confidence 22) interval for the true proportion of all adults in the town who have health insurance. A) < p < B) < p < C) < p < D) < p < ) Of 112 randomly selected adults, 34 were found to have high blood pressure. Construct a 95% confidence interval for the true percentage of all adults that have high blood pressure. 23) A) 19.1% < p < 41.6% B) 23.2% < p < 37.5% C) 21.8% < p < 38.9% D) 20.2% < p < 40.5% Solve the problem. 24) Find the critical value z /2 that corresponds to a degree of confidence of 91%. 24) A) 1.75 B) C) 1.34 D) 1.70 Determine whether the given conditions justify using the margin of error E = z /2 / interval estimate of the population mean µ. n when finding a confidence 25) The sample size is n = 205 and = ) A) Yes B) No 26) The sample size is n = 12, is not known, and the original population is normally distributed. 26) A) Yes B) No 3

4 Use the confidence level and sample data to find the margin of error E. 27) Weights of eggs: 95% confidence; n = 52, x = 1.78 oz, = 0.40 oz 27) A) 0.02 oz B) 0.11 oz C) 0.09 oz D) 7.21 oz 28) Systolic blood pressures for women aged 18-24: 94% confidence; n = 98, x = mm Hg, = 13.4 mm Hg 28) A) 50.3 mm Hg B) 9.9 mm Hg C) 2.2 mm Hg D) 2.5 mm Hg Use the confidence level and sample data to find a confidence interval for estimating the population µ. 29) Test scores: n = 95, x = 73.8, = 7.4; 99 percent 29) A) 72.5 < µ < 75.1 B) 71.8 < µ < 75.8 C) 72.3 < µ < 75.3 D) 72.0 < µ < ) A random sample of 194 full-grown lobsters had a mean weight of 21 ounces and a standard deviation of 3.8 ounces. Construct a 98 percent confidence interval for the population mean µ. 30) A) 20 < µ < 23 B) 21 < µ < 23 C) 20 < µ < 22 D) 19 < µ < 21 Use the margin of error, confidence level, and standard deviation to find the minimum sample size required to estimate an unknown population mean µ. 31) Margin of error: $124, confidence level: 95%, = $530 31) A) 62 B) 2 C) 5 D) 71 Do one of the following, as appropriate: (a) Find the critical value z /2, (b) find the critical value t /2, (c) state that neither the normal nor the t distribution applies. 32) 98%; n = 7; = 27; population appears to be normally distributed. 32) A) z /2 = 2.33 B) t /2 = 1.96 C) t /2 = D) z /2 = ) 99%; n = 17; is unknown; population appears to be normally distributed. 33) A) t /2 = B) t /2 = C) z /2 = D) z /2 = ) 95%; n = 11; is known; population appears to be very skewed. 34) A) z /2 = B) Neither the normal nor the t distribution applies. C) z /2 = 1.96 D) t /2 =

5 Find the margin of error. 35) 95% confidence interval; n = 91 ; _ x = 53, s = ) A) 2.60 B) 4.80 C) 2.23 D) ) 95% confidence interval; n = 51; _ x = 129; s = ) A) B) 77.1 C) 69.4 D) Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume that the population has a normal distribution. 37) A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was ) milligrams with s = 18.2 milligrams. Construct a 95 percent confidence interval for the true mean cholesterol content of all such eggs. A) < µ < B) < µ < C) < µ < D) < µ < ) A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is Construct the 95% confidence interval for the mean score of all such subjects. 38) A) 74.6 < µ < 77.8 B) 67.7 < µ < 84.7 C) 64.2 < µ < 88.2 D) 69.2 < µ <

6 Answer Key Testname: CH 7 SET 1 1) A point estimate is a single value used to approximate a population parameter. The sample mean x is the best point estimate of μ. 2) The margin of error is the maximum likely difference between the observed sample mean x and the true value for the population mean μ. The confidence interval is found by taking the sample mean x and adding the margin of error E to find the high value and subtracting E to find the low value of the interval. In the interval 9.65 < μ < 11.35, the sample mean x is 10.5 and the error estimate E is ) Provided n > 30, the standard normal distribution is the one to use. If n 30, the population must be normal and σ must be known to use the formula. 4) 1) Use the range rule of thumb. 2) Conduct a pilot study and base your estimate of σ on the first collection of at least 31 randomly selected values. 5) We are 95% sure that the interval contains the true population value for mean weekly salaries of shift managers at Guiseppeʹs Pizza and Pasta. 6) C 7) B 8) D 9) B 10) B 11) C 12) A 13) D 14) C 15) D 16) B 17) D 18) A 19) C 20) C 21) A 22) C 23) C 24) D 25) A 26) B 27) B 28) D 29) B 30) C 31) D 32) A 33) A 34) B 35) A 36) B 37) A 38) B 6

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