Question

theres five parts to this question if you know what the parts are, plewse answer them as well.. will give thumbs up. thank you

3 of 4 (1 complete) Score: 0 of 1 pt 9.2.17-T A simple random sample of size n is drawn from a population that is normally distributed The sample mean 2 is found to be 104, and the sample standard deviation, s. is found to be 11 (a) Construct a 95% confidence interval about if the sample sice, n, is 27 (b) Construct a 95% confidence interval about if the sample size. nis 16 (c) Construct a 90% confidence interval about if the sample size. nis 27 (d) Should the confidence intervals in parts (c) have been computed if the population had not been normally distributed? (a) Construct a 96% confidence interval about if the sample size, n, is 27 Lower bound Upper bound Round to one decimal place as needed) Enter your answer in the cat fields and then check Answer 5 remaining

Answer 1

(a)

Sample mean = 3 = 104 Sample size = n = 27 Sample S.D=s = 11 Standard Error = s/Vn = 11/27 = 2.12 Confidence Level = 96 Significance Level = Q = (100-96)% = 0.04 Degrees of freedom = n-1 = 27 -1 = 26 Critical value = t* = 2.162 [ using Excel =TINV(0.04,26)] Margin of Error = t* (s/Vn )= 2.162*2.12 = 4.58 Lower Limit = 3 - Margin of Error = 104 -4.58 = 99.4 Upper Limit = x + Margin of Error = 104 + 4.58 = 108.6

(b)

Sample mean = x = 104 Sample size = n = 16 Sample S.D = s = 11 Standard Error = s/Vn = 11/16 = 2.75 Confidence Level = 96 Significance Level = Q = (100-96)% = 0.04 Degrees of freedom = n-1 = 16-1 = 15 Critical value = ** = 2.249 [ using Excel =TINV(0.04,15)] Margin of Error = t*(s/Vn )= 2.249*2.75 = 6.18 Lower Limit = x - Margin of Error = 104 - 6.18 = 97.8 Upper Limit = x + Margin of Error = 104 + 6.18 = 110.2

(c)

Sample mean = x = 104 Sample size = n = 27 Sample S.D=s= 11 Standard Error = s/Vn = 11/127 = 2.12 Confidence Level = 90 Significance Level = Q = (100-90)% = 0.1 Degrees of freedom = n-1 = 27 -1 = 26 Critical value = t* = 1.706 [ using Excel =TINV(0.1,26)] Margin of Error = t*(s/Vn )= 1.706*2.12 = 3.62 Lower Limit = 7 - Margin of Error = 104 - 3.62 = 100.4 Upper Limit = x + Margin of Error = 104 + 3.62 = 107.6

(d) No, since sample sizes are less than 30.