Question

2. Given the following descriptive statistics,

N=18

X bar = 11.5

S sub x = 2

a. find the 95% confidence interval of the population mean u.

b. Suppose you know the population standard deviation = 2. What is the minimum sample size that makes the confidence interval length less than 1?

Answer 1

Given:

a) 95% confidence interval for population mean mu

The formula to find the confidence interval is,

To find t critical value, degrees of freedom = N - 1 = 18 - 1 = 17

The t critical value in two tailed area alpha as 0.05 and degrees of freedom 17 is, 2.110

Plugging all the values in the formula of confidence interval,

The 95% confidence interval for population mean is (10.505, 12.495)

b) Sample size

The formula to find sample size,

Where Z - critical value at given confidence level

To find it, find area 1 - alpha/2

alpha = 0.05

alpha/2 = 0.025

1 - (alpha/2) = 1 - 0.025 = 0.975

By using z table the z critical value for area 0.9750 is 1.96

E - margin of error that is half length of interval

length of interval = 1

E = Half length = 1/2 = 0.5

Plug all the values in the formula of n,

Minimum sample size required = 62