Asimple do sample of size n is draw from a population that is om ally distribute

Question

Asimple do sample of size n is draw from a population that is om ally distributed. The sample meanx.is found to be 110, and the sample standard deviation, s, is found to be 10. (a) Construct an 80% confidence interval about if the sample size, n, is 28 (b) Construct an 80% confidence interval abou tho sample size, n, is 19. (c) Construct a 70% confidence interval about ífth sample size, n, is 28. (d) Could we have computed the confidence intervals in parts (a)(c) i the population had not been normally distributed? Cick th on to view the table ofaroas under the t-distribution. (a) Construct an 80% confidence interval about if the sample size, n, is 28 Lower boundUpper bound: (Use ascending order. Round to one decimal place as needed) (b) Construct an 80% conidence interval about ,the sample size, n, is 19. Lower boundUpper bound: (Use ascending order Round to one decimal place as needed) How does decreasing the sample size affect the margin of ermor, E OA As the sample size decreases, the margin of error increases B. As the sample size decreases, the margin of error decreases O C. As the sample size decreases, the margin of error stays the same (c) Construct a 70% oorfidence interval abot-ifthe sample size, n, 28. Lower bound upper bound: (Use ascending order Round to one decimal place as needed. compare resu tothose otta ned in part(a). How does decreasing the level of confidence anect the size ofthe margin of omor, E? OA As the percent confidence decreases, the size of the interval decreases. B. As the percent oorndenco docroases, te sizo of the interval stays the same.

Explanation / Answer

a)

One-Sample T

N    Mean StDev SE Mean       80% CI
28 110.00 10.00     1.89 (107.52, 112.48)

b)

N    Mean StDev SE Mean       80% CI
19 110.00 10.00     2.29 (106.95, 113.05)

option A) is correct

sample size decrease ,margin of error increase

c)

N    Mean StDev SE Mean       70% CI
28 110.00 10.00     1.89 (108.00, 112.00)

option A) is correct

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