Question

A car company claims that its cars achieve an average gas mileage of at least 26 miles per gallon. A random sample of eight cars form this company have an average gas mileage of 25.2 miles per gallon and a standard deviation of 1 mile per gallon. At α=0.06, can the company’s claim be supported, assuming this is a normally distributed data set?

a) No, since the test statistic of -2.26 is in the rejection region defined by the critical value of -1.77, the null is rejected. The claim is the null, so is not supported

b) Yes, since the test statistic of -2.26 is not in the rejection region defined by the critical value of -1.77, the null is not rejected. The claim is the null, so is supported

c) Yes, since the test statistic of -2.26 is in the rejection region defined by the critical value of -1.55, the null is rejected. The claim is the null, so is supported

d) No, since the test statistic of -2.26 is not in the rejection region defined by the critical value of -1.24, the null is not rejected. The claim is the null, so is supported

Answer 1

The provided sample mean is Xˉ=25.2 and the sample standard deviation is s=1, and the sample size is n = 8

Ho: μ = 26

Ha: μ < 26

the critical value for a left-tailed test is tc​=−1.77.

t = -2.26

Since it is observed that t=−2.26 < tc​=−1.77  it is then concluded that the null hypothesis is rejected.

No, since the test statistic of -2.26 is in the rejection region defined by the critical value of -1.77, the null is rejected. The claim is the null, so is not supported

option A is correct

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