Question

According to a travel website, workers in a certain country lead the world in vacation days, averaging 21.02 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 8 9 13 18 22 29 16 28 17 23 26 34 30 30 38 56 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. What would happen to the width of the confidence interval if the level of confidence increased (assuming everything else remained the same)? O A. The width of the confidence interval would stay the same. B. More information is needed to determine how the width would change C. The width of the confidence interval would increase. D. The width of the confidence interval would decrease.

Answer 1

a. Lette where, se denote the average number of paid vacation days Bon workers from this country. As surning the datering coming from a normal. distribution we formula (a monia to 3en1) , ã than the co-)) sample mean-toxin me sample size. De sample standard deviation, 22C; – ) ? ->(342 ma?) to ; en-1), is upper 100 ) 9. point of tro distribution :: For 2-0-05, the 100(1-0)4.2959% confidence interval foro Me can be obtained, for- :(n-1) to.025;06-12 m-1 izl t0:05

Computation: n = 20 workers. ã=I 20 (8 +14+6 +28+8+26+ ... +28+56) 465 20 23.25 Ex? = (8?+1+2 +62+282 -- +282+562) z 13593 20-1) (13593 - (aox 23.758) $ ñ 12-09991 and , using table off t-distribution, with degrees of freedom (86) = (20-1)=19. t 0.025;19 ~ 2.093 :: Lower ümit 23.25 12.09991 -x2.093 120 14.59 1-043) : upper limit 12.09991 23:25 + x 2.093 120 28.91 Answer: The 95% confidence interval i8 : from 17:59 ]days to [28.91 days b. If level of confidence is increased assuming everything else remained the same, then- C. The cuidth of the confidence interval would increase

limit xt FC ro z Explanation: Confidence level = 100(1-0)% gives the width of the confidence intervall Cowero uppero nit limit g; (n-1) )-(x - vi og ; (M-1) 28 ป) As, 100(1-0)% increases, we see a decreases (:(1-0) will a decreases) "Keeping everything other than a fixed, we know- ; (n-1) increases, as a decreases. Hence, width will also increase. 69, (0-1) increase as

e. The troue Statements is; C. A confidence interval fora a population mean gives possible values for the 'troue population mean with a certain level of confidence. Explanation : It is an interval, so it contains all possible values of troue population mean, with a significance.