Give the values of the test statistic, and the p-value.

Question

in the 90's the mean number televisions in a household was 2.1.A sociologist believes that this number has increased significantly in the last 20 years. 50 households are randomly sampled in 2020. Of these sampled, these households had a mean of 3.2 televisions with a sample standard deviation of 0.5 televisions. Test the hypothesis that the mean number of televisions in a household has increased.

Answer 1

Hi Caroline.

In this scenario, I believe it will be a z-test. The null hypothesis would be equal to 2.1 (H₀: μ=2.1) while the alternate hypothesis would be greater than because the claim is that the amount of TVs would increase (H_a: μ>2.1).

If you have a TI-83 or 84, you can use the STAT feature to find the test statistic and p-value. On the calculator, you would hit STAT, then move over until TESTS is highlighted. Hit #1 then highlight Stats.

You would put μ₀=2.1, ο=0.5, x=3.2, n=50 and highlight >μ₀.

After you hit Calculate, the p-value they give is a 7.58E-55, therefore it is extremely small, basically 0. This means that the increase of TVs in households has indeed increased.