Question

Currently, the mean miles per gallon for a Nissan Sentra is 35.0 mpg. After making improvements, engineers found that for 23 randomly selected cars, the average miles per gallon is 36.8 with a standard deviation is 4.7. Assume that the samples come from normal populations. Find the ?-value for testing the claim that the mean miles per gallon has increased after making these improvements.

(A) 0.040

(B) 0.079

(C) 0.960

(D) 0.096

Answer 1

Solution :

Given that,

Population mean = = 35

Sample mean = = 36.8

Sample standard deviation = s = 4.7

Sample size = n = 23

This a right (One) tailed test.

The null and alternative hypothesis is,

Ho: 35

Ha: 35

The test statistics,

t = ( - )/ (s/)

= ( 36.8 - 35 ) / ( 4.7 /23)

= 1.837

p-value :

df = n - 1 = 22

p-value = 0.0399 ( using probability t- distribution table,)

= 0.040

Option A) is correct,