Question

records of 40 used passanger cars and 40 used pickup tricks were randomly selected to investigate whether there was any difference in the mean time in years that they were kept by original owner before being sold. For cars, the mean was 5.3 years with standard deviation 2.2 years. For pickup trucks, the mean was 7.1 years with standard deviation 3.0 years. Test the hypothesis that there is a difference in the means against the null hypothesis that there is no difference. Use the 1% level of significance.

Answer 1

There is significant difference between the two average times

Explanation:

This test would be comparison of two means where only sample variances and means are given.

Since variances are unequal we have to do t test for unequal variances.

`H_0: \bar x=\bar y\\H_a: \bar x\\eq \bar y\`

(Two tailed test)(x represents grou I cars, and Y group 2 trucks)

Group Group One Group Two

Mean 5.300 7.100

SD 2.200 3.000

SEM 0.348 0.474

N 40 40

The mean of Group One minus Group Two equals -1.800

standard error of difference = 0.588

t = 3.0601

df = 78

The two-tailed P value equals 0.0030

Since p <1% we reject null hypothesis

There is significant difference between the two average times