Question

More time on the Internet: A researcher polled a sample of 1012 adults in the year 2010, asking them how many hours per week they spent on the Internet. The sample mean was 10.01 with a standard deviation of 13.90. A second sample of 1011 adults was taken in the year 2012. For this sample, the mean was 9.66 with a standard deviation of 13.81. Assume these are simple random samples from populations of adults. Can you conclude that the mean number of hours per week spent on the Internet differs between 2010 and 2012? Let u, denote the mean number of hours spent on the Internet in 2010. Use the a=0.05 level and the P-value method with the TI-84 calculator.

State the appropriate null and alternate hypotheses.

Answer 1

To test whether the mean number of hours spent on the Internet changed from 2010 to 2012, we use the null hypothesis that the means are equal and the alternative hypothesis that they are not. Using a TI-84 calculator, we conduct a 2-Sample T-Test and compare the p-value to α = 0.05 to make a decision. If the p-value is less than 0.05, we conclude there is a significant difference.

Step-by-step explanation:

To determine whether the mean number of hours per week spent on the Internet differs between 2010 and 2012, we begin by stating the null and alternative hypotheses using μ, the mean number of hours spent on the Internet.

The null hypothesis (H0) is that the mean number of hours does not differ between the two years, which can be written as:

H0: μ2010 = μ2012

The alternative hypothesis (Ha) is that the mean number of hours does differ, which we specify as:

Ha: μ2010 ≠ μ2012

To perform the hypothesis test using the TI-84 calculator, you would:

1. Enter the sample means, standard deviations, and sizes for each sample.
2. Use the 2-Sample T-Test function since we don't know the population standard deviations and are using sample data.
3. Set the test for ≠ to test for any difference between the means.
4. Determine the p-value provided by the calculator.
5. Compare the p-value to the significance level α = 0.05 to decide whether to reject or fail to reject the null hypothesis.

If the p-value is less than 0.05, we reject the null hypothesis and conclude that there is a statistically significant difference between the mean number of hours spent on the Internet in 2010 and 2012. If the p-value is greater than 0.05, we fail to reject the null hypothesis and cannot conclude that there is a difference.