Question

Allstate Insurance is one of the major automobile insurance companies in the country, Recently the western region claims manager instructed an intern in her department to develop a confidence interval estimate of the difference between the mean years that male customers have been insured by Allstate versus female customers. The intern randomly selected 13 male and 13 female customers from the account records and the summary is given below (rounded to the nearest year)

Sample Mean - Male = 12, sample variance - male = 3

Sample Mean - Female = 7, Sample variance - female = 4

a) does this data suggest that there exists a difference in the average years insurance by Allstate between male and female? Use α = 0.05

b) find the p value for the test

Answer 1

H0: Null Hypothesis:

HA: Alternative Hypothesis:

Test statistic is given by:

t = (12 - 7)/0.7338 = 6.8136

= 0.05

ndf = n1+ n2 - 2= 13 + 13 - 2 =24

From Table,critical values of t = 2.0639

Since calculated value of t = 6.7338 is greater than critical value of t = 2.0639, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that there exists a difference in the average years insurance by Allstate between male and female.

(b)

t score = 6.7338

ndf = 24

Two Tail Test

By Technology, P- Value < 0.0001