Chapter 7 - Practice Problems 1

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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 < 11.35. 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.

325.80 < µ < 472.30

5)

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) 2.575 B) 2.05 C) 2.33 D) 1.75

7) Find the critical value z /2 that corresponds to a degree of confidence of 91%. 7)

A) 1.75 B) 1.70 C) 1.645 D) 1.34

Express the confidence interval in the form of p ± E.^

8) -0.134 < p < 0.666 8)

^ ^ ^ ^

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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) 0.718 B) 0.714 C) 0.728 D) 0.700

10) The following confidence interval is obtained for a population proportion, p:

0.478 < p < 0.510

Use these confidence interval limits to find the margin of error, E.

10)

A) 0.032 B) 0.016 C) 0.494 D) 0.017

Find the margin of error for the 95% confidence interval used to estimate the population proportion.

11) n = 151, x = 122 11)

A) 0.110 B) 0.00201 C) 0.0628 D) 0.0565

12) In a survey of 4800 T.V. viewers, 50% said they watch network news programs. 12)

A) 0.0141 B) 0.0106 C) 0.0162 D) 0.0185

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) 0.144 < p < 0.338 B) 0.126 < p < 0.356 C) 0.145 < p < 0.337 D) 0.127 < p < 0.355

14) n = 140, x = 81; 90 percent 14)

A) 0.514 < p < 0.644 B) 0.509 < p < 0.649 C) 0.510 < p < 0.648 D) 0.513 < p < 0.645

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) 5701

16) 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 0.22. 17)

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%. 18)

A) 1040 B) 1795 C) 936 D) 2476

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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) 0.128 B) 0.853 C) 0.147 D) 0.145

20) 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

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) 0.438 < p < 0.505 B) 0.444 < p < 0.500 C) 0.471 < p < 0.472 D) 0.435 < p < 0.508

22) Of 99 adults selected randomly from one town, 63 have health insurance. Find a 90% confidence

interval for the true proportion of all adults in the town who have health insurance. 22) A) 0.542 < p < 0.731 B) 0.524 < p < 0.749

C) 0.557 < p < 0.716 D) 0.512 < p < 0.761

23) 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%

24)Find the critical value z /2 that corresponds to a degree of confidence of 91%. 24)

A) 1.75 B) 1.645 C) 1.34 D) 1.70

Determine whether the given conditions justify using the margin of error E = z _/2 / n when finding a confidence interval estimate of the population mean µ.

25) The sample size is n = 205 and = 15. 25)

A) Yes B) No

26) The sample size is n = 12, is not known, and the original population is normally distributed. 26)

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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 = 113.1 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 < 75.6 30) 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 = 2.575 D) z /2 = 2.05

33) 99%; n = 17; is unknown; population appears to be normally distributed. 33) A) t /2 = 2.921 B) t /2 = 2.898 C) z /2 = 2.567 D) z /2 = 2.583

34) 95%; n = 11; is known; population appears to be very skewed. 34)

A) z /2 = 1.812

B) Neither the normal nor the t distribution applies.

C) z /2 = 1.96 D) t /2 = 2.228

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Find the margin of error.

35) 95% confidence interval; n = 91 ; _

x = 53, s = 12.5 35)

A) 2.60 B) 4.80 C) 2.23 D) 2.34

36) 95% confidence interval; n = 51; _

x = 129; s = 274 36)

A) 100.2 B) 77.1 C) 69.4 D) 161.9

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 208 milligrams with s = 18.2 milligrams. Construct a 95 percent confidence interval for the true mean cholesterol content of all such eggs.

37)

A) 196.4 < µ < 219.6 B) 198.6 < µ < 217.4 C) 196.3 < µ < 219.7 D) 196.5 < µ < 219.5

38) 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 21.4.

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 < 83.2

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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 0.85.

3) 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