Question

watching tv: the 2012 general social survey asked a large number of people how much time they spent watching tv each day. the mean number of hours was 3.09 with a standard deviation of 2.89. assume that in a sample of 33 teenagers, the sample standard deviation of daily tv time is 2.4 hours, and that the population of tv watching times is normally distributed. can you conclude that the population standard deviation of tv watching times for teenagers is less than 2.89? use the α = 0.05 level of significance. state the appropriate null and alternate hypotheses. h0: σ = 2.89 h1: σ < 2.89 select right - tailed, left - tailed, two - tailed test. this hypothesis test is a left - tailed test. part: 0 / 5 part 1 of 5

Explanation:

Step1: Define null and alternative hypotheses

The claim is that the population standard - deviation of TV watching times for teenagers is less than 2.89. The null hypothesis $H_0$ is the statement of no change or equality, and the alternative hypothesis $H_1$ is the claim we are trying to find evidence for. So, $H_0:\sigma = 2.89$ and $H_1:\sigma<2.89$.

Step2: Determine the type of test

Since the alternative hypothesis has a less - than sign ($<$), this is a left - tailed test.

Answer:

State the appropriate null and alternate hypotheses: $H_0:\sigma = 2.89$, $H_1:\sigma<2.89$
This hypothesis test is a left - tailed test.