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

ID: 3239460 • Letter: A

Question

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

x overbarx,

is found to be

107,

and the sample standard deviation, s, is found to be

10.

(a) Construct

90%

confidence interval about

if the sample size, n, is

12.

(b) Construct

90%

confidence interval about

if the sample size, n, is

17.

(c) Construct

99%

confidence interval about

if the sample size, n, is

12.

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

Here Xbar = 107 and s = 10

(a) Construct a 90% confidence interval about if the sample size, n, is 12.

90% CI = xbar +- t11,0.05 (s/n) = 107 +- 1.796 * (10/ 12)

= (101.815, 112.185)

(b) Construct a 90% confidence interval about if the sample size, n, is 17.

90% CI = xbar +- t11,0.05 (s/n) = 107 +- 1.796 * (10/ 17)

= (102.644, 111.356)

(c) Construct a 99% confidence interval about if the sample size, n, is 12.

99% CI = xbar +- t11,0.05 (s/n) = 107 +- 3.106 * (10/ 12)

= (98.034, 115.966)

(d) No, the sample sizes are too small to assume that mean of the samples will be normally distributed.

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