Question

We wish to test the claim that u>32 at a level of significance of a =.05. The sample statistics are n = 50 and x-bar = 32.3. Moreover, it is known that the population mean is 1.2.

Answer 1

To test whether u > 32 at a level of significance of a = .05, we set up the hypothesis test by comparing the test statistic to the critical value. If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that u > 32.

Step-by-step explanation:

To test the claim that u > 32 at a level of significance of a = .05, we set up the hypothesis test as follows:

H0: u = 32

Ha: u > 32

We calculate the test statistic using the sample statistics:

Test statistic = (x-bar - u) / (s / sqrt(n))

where x-bar is the sample mean, u is the population mean, s is the sample standard deviation, and n is the sample size.

Then, we compare the test statistic to the critical value of the t-distribution with (n-1) degrees of freedom at a = 0.05.

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that u > 32.

If the test statistic is less than or equal to the critical value, we fail to reject the null hypothesis and do not have enough evidence to support the claim.