A simple random sample of size n is drawn from a population that is normally dis
ID: 3362778 • Letter: A
Question
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 114, and the sample standard deviation, s, is found to be 10 (a) Construct a 98% confidence interval about if the sample size, n, is 22. (b) Construct a 98% confidence interval about if the sample size, n, is 18. (c) Construct a 96% confidence interval about if the sample size, n. is 22. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? Click the icon to view the table of areas under the t-distribution. (a) Construct a 98% confidence interval about if the sample size, n, is 22. Lower bound: 108.6: Upper bound: 119.4 (Use ascending order. Round to one decimal place as needed) (b) Construct a 98% confidence interval about if the sample size, n, is 18. Lower bound: D Upper bound: (Use ascending order. Round to one decimal place as needed.)Explanation / Answer
a) xbar= 114 and S=10, n=22 t = 2.52
sM = (10/22) = 0.67
= xbar ± t(sM)
= 114 ± 2.52*0.67
= 114 ± 1.7
xbar = 114, 98% CI [112.30,115.7].
You can be 98% confident that the population mean () falls between 112.30 and 115.7.
b) xbar= 114 ,S=10 , n= 18 and t= 2.57
sM = (10/18) = 0.74
= xbar ± t(sM)
= 114 ± 2.57*0.74
= 114 ± 1.91
xbar = 114, 98% CI [112.08,115.91].
You can be 98% confident that the population mean () falls between 112.08 and 115.91.
c) xbar= 114 ,S=10 , n= 22 and t= 1.99
sM = (10/22) = 0.67
= xbar ± t(sM)
= 114 ± 1.99*0.67
= 114 ± 1.33
xbar = 114, 96% CI [112.67,115.33].
You can be 96% confident that the population mean () falls between [112.67 and 115.33].
d) No we couldn't compute the confidence interval if the population had NOT been normally distributed
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