Question

1. Young children in the U.S. are exposed to an average of 4 hours of television per day, which can adversely impact a child’s well-being. You are working in a research lab that hypothesizes that children in low income households are exposed to more than 4 hours of television. In order to test this hypothesis, you collected data on a random sample of 75 children from low income households. You found a sample mean television exposure time of 4.5 hours. Based on a previous study, you are willing to assume a population standard deviation of 0.5 hours. a. Using this information, test your hypothesis using the critical value approach; assume a significance level of 10%. b. Calculate the p-value associated with your test statistic. Using the p-value approach, what is your hypothesis test conclusion?

Answer 1

The provided sample mean is 4.5 and the sample standard deviation is 0.5, and the sample size is n = 75.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ = 4

Ha: μ > 4

This corresponds to a right-tailed test, for which a t-test for one mean, with unknown population standard deviation, will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.1, and the critical value for a right-tailed test is t_c = 1.293.

(3) Test Statistics

The t-statistic is computed as follows:

(4) Decision about the null hypothesis

Using the P-value approach: The p-value is p = 0 , and since p = 0 < 0.1, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is greater than 4, at the 0.1 significance level.