Question

I would like to test the null hypothesis that the population mean is 50 versus the alternative that it is not 50. My sample size is 6 and the sample mean is 38 with sample standard deviation of 16. At α = 0.05, I should:

Group of answer choices

Strongly reject the null hypothesis

Mildly reject the null hypothesis

Fail to reject the null hypothesis

Accept the alternative hypothesis

There is insufficient information to determine

Answer 1

Given that, sample size (n) = 6, sample mean = 38 and

sample standard deviation (s) = 16

The null and alternative hypotheses are,

H0 : μ = 50

Ha : μ ≠ 50

This hypothesis test is a two-tailed test.

Test statistic is,

=> Test statistic = t = -1.837

Degrees of freedom = 6 - 1 = 5

Using t-table we get, t-critical values at significance level of 0.05 with 5 degrees of freedom are, tcrit = ± 2.571

Since, test statistic = -1.837 > -2.571, we fail to reject H0.

Answer : Fail to reject the null hypothesis.