Question

Suppose you take a random sample of 30 individuals from a large population. For this sample, the sample mean is 4.2 and sample variance is 49. You wish to estimate the unknown population mean µ.

(a) Calculate a 90% confidence interval for µ.

(b) Calculate a 95% confidence interval for µ.

(c) Based on (a) and (b), comment on what happens to the width of a confidence interval (increase/decrease) when you increase your confidence level.

(d) Suppose your sample size is 100 instead of 30. The sample mean and variance are still 4.2 and 49 respectively. Calculate a new 90% confidence interval for µ.

(e) Based on (a) and (d), comment on what happens to the width of a confidence interval (increase/decrease) when you increase your sample size.

Answer 1

Given that

sample n =30

sample mean μ,=4.2

sample variance σ^2= 49

standard deviation σ = 7

a)

b)

c)  The width increases as the confidence level increase

d)

e)

Increasing the sample size decreases the width of confidence intervals