According to a travel website, workers in a certain country lead the world in va

Question

According to a travel website, workers in a certain country lead the world in vacation days, averaging 23.97 days per year. The following data show the number of paid vacation days for a random sample of 20 workers from this country. Complete parts a through c below. 6 2 5 4 10 22 21 27 18 26 17 29 21 21 30 34 28 28 35 55 a. Construct a 95% confidence interval to estimate the average number of paid vacation days for workers from this country. The 95% confidence interval to estimate the average number of paid vacation days for workers from this country is from days to days. (Round to two decimal places as needed.) b. Do the results from this sample validate the website's findings? A. Since the population mean, 23.97, is contained within the 95% confidence interval, it can be said with 95% confidence that the sample does not validate the website's findings. B. Since the population mean, 23.97, is contained within the 95% confidence interval, it can be said with 95% confidence that the sample validates the website's findings. C. Since the population mean, 23.97, is not contained within the 95% confidence interval, it can be said with 95% confidence that the sample does not validate the website's findings. D. Since the population mean, 23.97, is not contained within the 95% confidence interval, it can be said with 95% confidence that the sample validates the website's findings. c. What assumptions need to be made about this population?

Explanation / Answer

a) Sample mean calculated as = 21.95

Standard deviation calculated as = 12.74228

We will use T distribution to calculate the Confidence interval

degree of freedom = 20-1 = 19

Margin of error = (2.093024*12.74228)/sqrt(20) = 5.963572

95% Interval

(21.95-5.963572, 21.95+5.963575)

= (15.99, 27.91)

b) Option B is Correct

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