Question

Let mu denote the true average number of minutes of a television commercial. Suppose the hypothesis H0: mu = 2.1 versus Ha: mu > 2.1 are tested. Assuming the commercial time is normally distributed, give the appropriate rejection region when there is a random sample of size 20 from the population and we would like to test at the level of significance 0.01. Let T be the appropriate test statistic.

A, T > 2.539
B. > 2.845
C. T> .528D. T >2.861

Answer 1

A. T > 2.539

Explanation:

We have a hypothesis test of the mean, with unknown population standard deviation.

The hypothesis are:

`H_0: \mu = 2.1 \\\\H_a: \mu > 2.1`

From the hypothesis we can see that the test is right-tailed, so the critical value of t should be a positive value.

The degrees of freedom can be calculated as:

`df=n-1=20-1=19`

The significance level is 0.01, so the critical value tc should be the one that satisfies:

`P(t>t_c)=0.01`

Looking up in a t-table, for 19 degrees of freedom, this critical value is tc=2.539.