A simple random sample of size n is drawn from a population that is normally dis

ID: 3291522 • Letter: A

Question

A simple random sample of size n is drawn from a population that is normally distributed. The sample mean,

overbarx, is found to be 107, and the sample standard deviation, s, is found to be 10.

(a) Construct a 98% confidence interval about if the sample size, n, is 27.

(b) Construct a 98% confidence interval about if the sample size, n, is 11.

(c) Construct a 70% confidence interval about if the sample size, n, is 27.

(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?

a) 98% confidence interval: (102.230, 111.770)

b) 98% confidence interval: (98.667, 115.333)

c) 70% confidence interval: (103.704, 11.296)

d) No, because the sample sizes are less than 30, population must have the normal distribution.

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