Question

A car manufacturer, Swanson, claims that the mean lifetime of one of its car engines is greater than 220000 miles, which is the mean lifetime of the engine of a competitor. The mean lifetime for a random sample of 23 of the Swanson engines was with mean of 226450 miles with a standard deviation of 11500 miles. Test the Swanson's claim using a significance level of 0.01. What is your conclusion?

Answer 1

Solution :

The null and alternative hypotheses would be as follows:

Test statisic :

To test the hypothesis the most appropriate test would be one sample t-test. The test statistic is given as follows:

Where, x̅ is sample mean, μ​​​​​ is hypothesized value of population mean under H​​​​0, s is sample standard deviation and n is sample size.

We have,  x̅ = 226450,  μ = 220000, s = 11500, n = 23

The value of the test statistic is 2.6898.

P - value :

Since, our test is right-tailed test, therefore we shall obtain right-tailed p-value for the test statistic. The right-tailed p-value is given as follows :

p-value = P(T > t)

p-value = P(T > 2.6898)

p-value = 0.0067

The p-value is 0.0067.

Significance level (α) = 0.01

(0.0067 < 0.01)

Since, p-value is less than the significance level of 0.01, therefore we shall reject the null hypothesis (H​​​​​​​​​​​0) at 0.01 level.

Conclusion : At 0.01 significance level, there is sufficient evidence to support the Swanson's claims that the mean lifetime of one of its car engines is greater than 220000 miles.