# 7.2 STATISTICS HOMEWORK - ESTIMATING A POPULATION MEAN

Assume that we want to construct a confidence interval. Do one of the​ following, as​ appropriate: (a) find the critical value α/2​, (b) find the critical value zα/2​, or​ (c) state that neither the normal distribution nor the t distribution applies.
The confidence level is
90​%, σ is not​ known, and the normal quantile plot of the 17 salaries​ (in thousands of​ dollars) of basketball players on a team is as shown.
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Assume that we want to construct a confidence interval. Do one of the​ following, as​ appropriate: (a) find the critical value α/2​, (b) find the critical value zα/2​, or​ (c) state that neither the normal distribution nor the t distribution applies.
The confidence level is
90​%, σ is not​ known, and the normal quantile plot of the 17 salaries​ (in thousands of​ dollars) of basketball players on a team is as shown.
Assume that we want to construct a confidence interval. Do one of the​ following, as​ appropriate: (a) find the critical value tα/2​, ​(b) find the critical value zα/2​, or​ (c) state that neither the normal distribution nor the t distribution applies.
The confidence level is 95​%, σ is not​ known, and the histogram of 59 player salaries​ (in thousands of​ dollars) of football players on a team is as shown.
Assume that we want to construct a confidence interval. Do one of the​ following, as​ appropriate: (a) find the critical value tα/2​, ​(b) find the critical value zα/2​, or​ (c) state that neither the normal distribution nor the t distribution applies.
The confidence level is 99​%, σ=3702 thousand​ dollars, and the histogram of 54 player salaries​ (in thousands of​ dollars) of football players on a team is as shown.
Assume that we want to construct a confidence interval. Do one of the​ following, as​ appropriate: (a) find the critical value tα/2​, ​(b) find the critical value zα/2​, or​ (c) state that neither the normal distribution nor the t distribution applies.
Here are summary statistics for randomly selected weights of newborn​ girls: n=296​, x=28.9 ​hg, s=7.3 hg. The confidence level is 95​%.
Here are summary statistics for randomly selected weights of newborn​ girls:
n=197​, x=32.1 ​hg, s=6.9 hg. Construct a confidence interval estimate of the mean. Use a 90​%confidence level. Are these results very different from the confidence interval 31.2hg<μ<33.4
hg with only 16 sample​ values,
x=32.3 ​hg, and s=2.5 hg?

a. What is the confidence interval for the population mean μ​?

b. Are the results between the two confidence intervals very different?
A data set includes
108 body temperatures of healthy adult humans having a mean of
98.2°F and a standard deviation of
0.64°F. Construct a 99​% confidence interval estimate of the mean body temperature of all healthy humans. What does the sample suggest about the use of 98.6°F as the mean body​ temperature?

a. What is the confidence interval estimate of the population mean
μ​?

b. What does this suggest about the use of 98.6°F as the mean body​ temperature?
A food safety guideline is that the mercury in fish should be below 1 part per million​ (ppm). Listed below are the amounts of mercury​ (ppm) found in tuna sushi sampled at different stores in a major city. Construct a 98​% confidence interval estimate of the mean amount of mercury in the population. Does it appear that there is too much mercury in tuna​ sushi?
0.55
0.76
0.10
0.94
1.37
0.52
0.85

a. What is the confidence interval estimate of the population mean
μ​?

b. Does it appear that there is too much mercury in tuna​ sushi?
An IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 90​%
confidence that the sample mean is within 8 IQ points of the true mean. Assume that σ=15 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.