Question

An automobile manufacturer claims that its van has a 37.4 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 280 vans, they found a mean MPG of 37.8. Assume the standard deviation is known to be 2.3. A level of significance of 0.05 will be used. Find the value of the test statistic. Round your answer to 2 decimal places. Enter the value of the test statistic.

Answer 1

Solution :

= 37.4

= 37.8

= 2.3

n = 280

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 37.4

H_a :     37.4

Test statistic = z

= ( - ) / / n

= (37.8-37.4-) /2.3 / 208 =2.508

= 2.51

P(z > 2.51 ) = 1 - P(z < 2.51 ) = 0.0121

P-value = 0.0121

= 0.05  

p = 0.0121 < 0.05, it is concluded that the null hypothesis is rejected