Question

overweight men for a random sample of 50 overweight men, the mean of the number of pounds that they were español overweight was 29. the standard deviation of the population is 3.8 pounds.
part 1 of 4
(a) the best point estimate of the mean is 29 pounds.
part 2 of 4
(b) find the 90% confidence interval of the mean of these pounds. round intermediate answers to at least three decimal places. round your final answers to one decimal place.
28.1 < μ < 29.9
part: 2 / 4
part 3 of 4
(c) find the 95% confidence interval of the mean of these pounds. round intermediate answers to at least three decimal places. round your final answers to one decimal place.
< μ <

Explanation:

Step1: Find the critical value \(z\)

For a \(95\%\) confidence interval, the significance level \(\alpha = 1 - 0.95=0.05\). Then \(\alpha/2=0.025\).
Looking up in the standard normal distribution table, \(z_{\alpha/2}=z_{0.025} = 1.96\)

Step2: Calculate the margin of error \(E\)

The formula for the margin of error when the population standard deviation \(\sigma\) is known is \(E = z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}\)
Given \(n = 50\), \(\sigma=3.8\), \(z_{\alpha/2}=1.96\)

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Step3: Calculate the confidence interval

The confidence interval formula is \(\bar{x}-E<\mu<\bar{x} + E\)
Given \(\bar{x}=29\)

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So the \(95\%\) confidence interval is \(28.0<\mu <30.0\)

Answer:

\(28.0<\mu <30.0\)