Question

. A researcher wishes to see if the mean number of days that a basic, low-price, small automobile sits on a dealer’s lot is 29. A sample of 30 automobile dealers has a mean of 30.1 days for this type of automobile. At an alpha 0f 0.05, test the claim that the meantime is greater than 29 days. The standard deviation (sigma) of the population is 3.8 days.

a. Support the claim b. Do not support the claim

Answer 1

Solution :

Given that,

Population mean = = 29

Sample mean = = 30.1

Population standard deviation = = 3.8

Sample size = n = 30

Level of significance = = 0.05

This a right (One) tailed test.

The null and alternative hypothesis is,  

Ho: 29

Ha: 29

The test statistics,

Z =( - )/ (/n)

= ( 30.1 - 29 ) / ( 2.8 / 30 )

= 1.59

P- Value = P(Z > z )

= 1 - P(Z < 1.59 )

= 1 - 0.9441

= 0.0559

The p-value is p = 0.0559, and since p = 0.0559 > 0.05 , it is concluded that the null hypothesis is fail to rejected.

b. Do not support the claim