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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Neither the normal distribution nor the t distribution

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.

tα/2 = 2.00; InvT(0.975,58)

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.

zα/2 = 2.58; InvNorm(0.005,0,1)

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%.

1.97; t = α/2 - InvT(0.975,295)

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. 31.3 hg <μ< 32.9 hg
T int, stats, enter values

b. No, because the confidence interval limits are similar.

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. 98.038F<mu<98.362F

b. This suggests that the mean body temperature
is lower than 98.6°F.

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?

a. (0.256, 1.198); enter data into L1, run TInt test, enter as data.

b. Yes, because it is possible that the mean is greater than 1 ppm. Also, at least one of the sample values exceeds 1 ppm, so at least some of the fish have too much mercury.

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.

a. 10 - use sample size formula

b. This number of IQ test scores is a fairly
small
number.

Salaries of 39 college graduates who took a statistics course in college have a mean, x, of $66,500.
Assuming a standard deviation,
σ, of $18,766, construct a
99% confidence interval for estimating the population mean μ.

Use E = tα/2 x s/sqrt of n ; lower limit: x-E; upper limit: x+E

The _______ is the best point estimate of the population mean.

sample mean

7.2 STATISTICS HOMEWORK - ESTIMATING A POPULATION MEAN

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