Question

In a random sample of five people, the mean driving distance to work was 25.4 miles and the standard deviation was 5.2 miles. Assume the random variable is normally distributed and use a t-distribution to find the margin of error and construct confidence intervals for the population mean at the following confidence levels:

a. 85%

b. 90%

c. 99%

Answer 1

Solution :

Given that,

a.

t /2,df = 1.778

Margin of error = E = t/2,df * (s /n)

= 1.778 * (5.2 / 5)

Margin of error = E = 4.1

b.

t /2,df = 2.132

Margin of error = E = t/2,df * (s /n)

= 2.132 * (5.2 / 5)

Margin of error = E = 5.0

c.

t /2,df = 4.609

Margin of error = E = t/2,df * (s /n)

= 4.609 * (5.2 / 5)

Margin of error = E = 10.7