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Chapter 7: Estimating Parameters and Determining Sample Sizes

Q6

Page 340

In Exercises 5鈥8, use the given information to find the number of degrees of freedom, the critical values L2andR2, and the confidence interval estimate of . The samples are from Appendix B and it is reasonable to assume that a simple random sample has been selected from a population with a normal distribution.

Weights of Pennies 95% confidence;n= 37,s= 0.01648 g.

Q6

Page 328

Using Correct Distribution. In Exercises 5鈥8, assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) Find the critical value t2,(b) find the critical value z2,or (c) state that neither the normal distribution nor the t distribution applies.

Denver Bronco Salaries confidence level is 90%, is not known, and the histogram of 61 player salaries (thousands of dollars) is as shown.

Q6

Page 311

Finding Critical Values. In Exercises 5鈥8, find the critical value that corresponds to the given confidence level.

99%

Q7

Page 311

Finding Critical Values. In Exercises 5鈥8, find the critical value that corresponds to the given confidence level.

99.5%

Q7

Page 347

In Exercises 5鈥8, use the relatively small number of given bootstrap samples to construct the confidence interval. Freshman 15: Here is a sample of amounts of weight change (kg) of college students in their freshman year (from Data Set 6 鈥淔reshman 15鈥 in Appendix B): 11, 3, 0, -2, where -2 represents a loss of 2 kg and positive values represent weight gained. Here are ten bootstrap samples: {11, 11, 11, 0}, {11, -2, 0, 11}, {11, -2, 3, 0}, {3, -2, 0, 11}, {0, 0, 0, 3}, {3, -2, 3, -2}, {11, 3, -2, 0}, { -2, 3, -2, 3}, { -2, 0, -2, 3}, {3, 11, 11, 11}. a. Using only the ten given bootstrap samples, construct an 80% confidence interval estimate of the mean weight change for the population. b. Using only the ten given bootstrap samples, construct an 80% confidence interval estimate of the standard deviation of the weight changes for the population.

Q7

Page 340

In Exercises 5鈥8, use the given information to find the number of degrees of freedom, the critical values X2 L and X2R, and the confidence interval estimate of . The samples are from Appendix B and it is reasonable to assume that a simple random sample has been selected from a population with a normal distribution.

Platelet Counts of Women 99% confidence;n= 147,s= 65.4.

Q8

Page 311

Finding Critical Values. In Exercises 5鈥8, find the critical value z2that corresponds to the given confidence level.

98%

Q9

Page 311

Formats of Confidence Intervals.

In Exercises 9鈥12, express the confidence interval using the indicated format. (The confidence intervals are based on the proportions of red, orange, yellow, and blue M&Ms in Data Set 27 鈥淢&M Weights鈥 in Appendix B.)

Red M&Ms Express 0.0434 < p < 0.217 in the form ofp+E

Q9

Page 328

Confidence Intervals. In Exercises 9鈥24, construct the confidence interval estimate of the mean.

Birth Weights of Girls Use these summary statistics given in Exercise 8:n=205,x=30.4hg,s=7.1hg. Use a 95% confidence level. Are the results very different from those found in Example 2 with only 15 sample values?

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