Question

In the year 2000, the average vehicle had a fuel economy of 24.84 MPG. You are curious as to whether the average in the present day is different from the historical value. The hypotheses for this scenario are as follows: Null Hypothesis: μ = 24.84, Alternative Hypothesis: μ ≠ 24.84. A random sample of 37 vehicles shows an average economy of 25.99 MPG with a standard deviation of 4.915 MPG. What is the test statistic and p-value for this test?

Answer 1

Solution :

Given that,

Population mean = = 24.84

Sample mean = = 25.99

Sample standard deviation = s = 4.915

Sample size = n = 37

This is a two tailed test.

The test statistics,

t = ( - )/ (s/)

= (25.99 - 24.84 ) / (4.915 /37)

= 1.423

The test statistic is 1.423

p-value:

df = n - 1 = 36

p-value = 0.1633

The p-value is 0.1633

( To see the p-value in probability t distribution table , using test statistic and degrees of freedom)