6) A random sample of 20 ages of world leaders yielded the following data: 54 66 53 49 50 65 82 62 65 63 47 76 68 71 72 78 77 88 72 59 a) Determine a 95% confidence interval for all the mean ages, , for all world leaders. Assume the population standard deviation is 11.2 years. (Note: the sum of the data is 1317.) b) Interpret your answer to part (a). 7) In a study, a sample of 26 students at a community college had a mean daily study time of 44.6 minutes. a) Assuming the study time of community college students is normally distributed with a standard deviation of 10.2 minutes, determine a 90% confidence interval for the mean daily study time of all community college students. b) Obtain the margin of error, E, for the confidence interval you found in (a). c) Explain the meaning of E in this context in terms of the accuracy of the estimate. d) Determine the sample size required to have a margin of error of 2.3 minutes with a 95% confidence interval. 8) A sample of 30 commuters in the New York City area yielded the following commute times in minutes: 45 25 26 27 34 56 44 36 50 32 28 48 25 40 35 36 46 28 30 28 30 24 50 32 32 27 29 27 22 40 a) Find a 90% confidence interval for the mean commute time of all commuters in New York City. (Note: ) b) Interpret your answer to part (a). 9) Provided below is the obtained value for the test statistic for a one-mean z-test. Determine the P-value in each case and determine whether, at the 5% significance level, the data provide sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis. Two tailed test: a) z=-2.04 b) z=1.90 10) The average consumer unit spent $1749 on apparel and services in 2012. That same year, 25 consumer units in the Northwest had the following annual expenditures, in dollars, on apparel and services. 1292 1470 2033 1695 1286 2236 2246 2205 1624 1747 2701 2042 2179 1873 2457 1857 1778 2280 1535 2025 2003 1764 2126 2215 1725 At the 5% significance level, do the data provide sufficient evidence to conclude that the 2012 mean annual expenditure on apparel and services for consumer units in the Northwest differed from the national mean of $1749? (Note: )

6) A random sample of 20 ages of world leaders yielded the following data: 54 66 53 49 50 65 82 62 65 63 47 76 68 71 72 78 77 88 72 59 a) Determine a 95% confidence interval for all the mean ages, , for all world leaders. Assume the population standard deviation is 11.2 years. (Note: the sum of the data is 1317.) b) Interpret your answer to part (a). 7) In a study, a sample of 26 students at a community college had a mean daily study time of 44.6 minutes. a) Assuming the study time of community college students is normally distributed with a standard deviation of 10.2 minutes, determine a 90% confidence interval for the mean daily study time of all community college students. b) Obtain the margin of error, E, for the confidence interval you found in (a). c) Explain the meaning of E in this context in terms of the accuracy of the estimate. d) Determine the sample size required to have a margin of error of 2.3 minutes with a 95% confidence interval. 8) A sample of 30 commuters in the New York City area yielded the following commute times in minutes: 45 25 26 27 34 56 44 36 50 32 28 48 25 40 35 36 46 28 30 28 30 24 50 32 32 27 29 27 22 40 a) Find a 90% confidence interval for the mean commute time of all commuters in New York City. (Note: ) b) Interpret your answer to part (a). 9) Provided below is the obtained value for the test statistic for a one-mean z-test. Determine the P-value in each case and determine whether, at the 5% significance level, the data provide sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis. Two tailed test: a) z=-2.04 b) z=1.90 10) The average consumer unit spent $1749 on apparel and services in 2012. That same year, 25 consumer units in the Northwest had the following annual expenditures, in dollars, on apparel and services. 1292 1470 2033 1695 1286 2236 2246 2205 1624 1747 2701 2042 2179 1873 2457 1857 1778 2280 1535 2025 2003 1764 2126 2215 1725 At the 5% significance level, do the data provide sufficient evidence to conclude that the 2012 mean annual expenditure on apparel and services for consumer units in the Northwest differed from the national mean of $1749? (Note: )

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 58E: What is meant by the sample space of an experiment?

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Question

6) A random sample of 20 ages of world leaders yielded the following data:

54 66 53 49 50

65 82 62 65 63

47 76 68 71 72

78 77 88 72 59

a) Determine a 95% confidence interval for all the mean ages, , for all world leaders. Assume the population standard deviation is 11.2 years. (Note: the sum of the data is 1317.)
b) Interpret your answer to part (a).

7) In a study, a sample of 26 students at a community college had a mean daily study time of 44.6 minutes.

a) Assuming the study time of community college students is normally distributed with a standard deviation of 10.2 minutes, determine a 90% confidence interval for the mean daily study time of all community college students.
b) Obtain the margin of error, E, for the confidence interval you found in (a).
c) Explain the meaning of E in this context in terms of the accuracy of the estimate.
d) Determine the sample size required to have a margin of error of 2.3 minutes with a 95% confidence interval.

8) A sample of 30 commuters in the New York City area yielded the following commute times in minutes:

45 25 26 27 34 56

44 36 50 32 28 48

25 40 35 36 46 28

30 28 30 24 50 32

32 27 29 27 22 40

a) Find a 90% confidence interval for the mean commute time of all commuters in New York City. (Note: )
b) Interpret your answer to part (a).

9) Provided below is the obtained value for the test statistic for a one-mean z-test. Determine the P-value in each case and determine whether, at the 5% significance level, the data provide sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.

Two tailed test:

a) z=-2.04
b) z=1.90

10) The average consumer unit spent $1749 on apparel and services in 2012. That same year, 25 consumer units in the Northwest had the following annual expenditures, in dollars, on apparel and services.

1292 1470 2033 1695 1286

2236 2246 2205 1624 1747

2701 2042 2179 1873 2457

1857 1778 2280 1535 2025

2003 1764 2126 2215 1725

At the 5% significance level, do the data provide sufficient evidence to conclude that the 2012 mean annual expenditure on apparel and services for consumer units in the Northwest differed from the national mean of $1749? (Note: )

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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