Question

A market researcher collects a simple random sample o customers from a population o over a million customers that use a home improvement website. After analyzing the sample, she states that she has 95% confidence that the mean time customers spent on that website per day is between 17 and 52 minutes. Suppose that the population mean time customers spent on that website is 49 minutes a day. Does this value of the population mean help to show that the confidence interval estimate is correct? Explain Choose the correct answer below. O A. O B. ° C. 0 D. O E. No, because the population mean, μ, is not in the middle half of the confidence interval estimate. Yes, because the population mean, μ s within 95% of the midpoint of the confidence interval estimate No, because the population mean, μ. is not the midpoint of the confidence interval estimate. Yes, because the population mean, μ, is included within the confidence interval estimate No, because the population mean, и. is not included within the confidence interval estimate.

Answer 1

Question 1:

Option D is correct.

Question 2:

As, $\sigma$ is known it is a z-test.

z value with 95% confidence interval (two tailed test), $z_{\alpha/2}$ = 1.96 (where $\alpha$ = 0.05)

So margin of error,

$M = z_{\alpha/2} \frac{\sigma}{\sqrt n} = 1.96 * \frac{6}{\sqrt{69}} = 1.4157$

Left limit = $\bar x$ - M = 101 - 1.4157 = 99.58

Right Limit = $\bar x$ + M = 101 + 1.4157 = 102.42

So, $99.58 \leq \mu \leq 102.42$ (Ans)

** If any answer does not match please comment.