Question

An automobile manufacturer claims that its jeep has a 53.9 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating. After testing 110 jeeps, they found a mean MPG of 53.7. Assume the standard deviation is known to be 1.8. A level of significance of 0.02 will be used.

Find the value of the test statistic.

Answer 1

Value of the test statistic,
`z_(test) = - 1.17`

Explanation:

Null hypothesis,
`H_(0): \mu = 53.9`

Alternative hypothesis,
`H_(a) : \mu \\eq 53.9`

Sample mean,
`\bar{X} = 53.7`

Sample size, n = 110

Standard deviation,
`\sigma = 1.8`

Significance level,
`\alpha = 0.02`

The value of the test statistics is given by the formula:

`z_(test) = \frac{\bar{X} - \mu}{(\sigma)/(√(n) ) } \\z_(test) = (53.7 - 53.9)/((1.8)/(√(110) ) ) \\z_(test) = - 1.17`