Question

A recent study compared the time spent together by single- and dual-earner couples. According to the records kept by the wives during the study, the mean amount of time spent together watching television among the single-earner couples was 61 minutes per day, with a standard deviation of 15.5 minutes. For the dual-earner couples, the mean number of minutes spent watching television was 48.4 minutes, with a standard deviation of 18.1 minutes.

At the .01 significance level, can we conclude that the single-earner couples on average spend more time watching television together? There were 15 single-earner and 12 dual-earner couples studied. Hint: For the calculations, assume the single-earner as the first sample.


This is a ____ twoone-tailed test.

Answer 1

The question is about conducting a one-tailed hypothesis test at the 0.01 significance level to see if single-earner couples watch more TV than dual-earner couples. We compare means using the formula for two independent samples, but without specific values for the test statistic calculation, if the test statistic exceeds the critical value, we reject the null hypothesis.

Step-by-step explanation:

The question deals with the hypothesis testing in statistics, specifically with comparing the mean time spent watching television between single- and dual-earner couples. Since the inquiry is to determine if single-earner couples spend more time watching television, this is a one-tailed test.

To solve the question, we set up our null hypothesis (H0) that there is no difference in mean watching time between single- and dual-earner couples (μ1 = μ2), and the alternative hypothesis (Ha) that single-earner couples watch television for a longer time (μ1 > μ2).

Given the sample sizes, means, and standard deviations, we calculate the test statistic using the formula for two independent samples. With the calculated test statistic and the degrees of freedom, we then determine the critical value from the t-distribution at the 0.01 significance level. If the test statistic exceeds the critical value, we reject the null hypothesis.

Since the question did not provide specific values for the test statistic calculation or outcomes, we cannot provide a conclusion on whether the hypothesis is rejected or not without this information.