Question

For this question assume that we have a random sample from a normal distribution with

unknown mean but known variance.

(a) Suppose that we have 36 observations, the sample mean is 5, and the population

variance is 9. Construct a 95% confidence interval for the population mean.

(b) Repeat the preceding with a population variance of 25 rather than 9.

(c) Repeat the preceding with a sample size of 25 rather than 36.

(d) Repeat the preceding but construct a 50% rather than 95% confidence interval.

(e) Repeat the preceding but construct a 99% rather than a 50% confidence interval.

Answer 1

a)

Mean = 5

Sample size (n) = 36

Standard deviation (s) =

Confidence interval(in %) = 95

z @ 95.0% = 1.96

Since we know that

Required confidence interval

Required confidence interval = (5.0-0.98, 5.0+0.98)

Required confidence interval = (4.02, 5.98)

b)

Mean = 5

Sample size (n) = 36

Standard deviation (s) =

Confidence interval(in %) = 95

z @ 95.0% = 1.96

Since we know that

Required confidence interval

Required confidence interval = (5.0-1.6333, 5.0+1.6333)

Required confidence interval = (3.3667, 6.6333)

c)

Mean = 5

Sample size (n) = 25

Standard deviation (s) =

Confidence interval(in %) = 95   

Since we know that

Required confidence interval   

Required confidence interval = (5.0-2.0639, 5.0+2.0639)

Required confidence interval = (2.9361, 7.0639)

d)

Mean = 5

Sample size (n) = 25

Standard deviation (s) =

Confidence interval(in %) = 50   

Since we know that

Required confidence interval   

Required confidence interval = (5.0-0.6848, 5.0+0.6848)

Required confidence interval = (4.3152, 5.6848)

e)

Mean = 5

Sample size (n) = 25

Standard deviation (s) =

Confidence interval(in %) = 99

Since we know that

Required confidence interval   

Required confidence interval = (5.0-2.7969, 5.0+2.7969)

Required confidence interval = (2.2031, 7.7969)

Please hit thumps up if the answer helped you.