A recent study compared the time spent together by single and dual-earner couples. According to the records kept during the study, the mean amount of time spent together watching TV among single-earner couples was 60 minutes per day, with a standard deviation of 15.5 minutes. For the dual-earner couples, the mean time was 48.4 and the standard deviation was 18.1. At a 0.01 significance level, can we conclude that the single-earner couples on average spend more time watching TV together? There were 12 single-earner and 12 dual-earner couples studied. State the decision rule, the value of the test statistic, and your decision.
A) Reject if t 2.485, t = 2.77, single-earner couples spend more time watching TV together.
B) Reject if t 2.508, t = 1.96, insufficient evidence to say that single-earner couples spend more time watching TV together.
C) Reject if t 2.797, t = 2.57, single-earner couples spend more time watching TV together.
D) Reject if t 2.508, t = 1.69, insufficient evidence to say that single-earner couples spend more time watching TV together.
E) Reject if t 2.508, t = 0.96, insufficient evidence to say that single-earner couples spend more time watching TV together.

Question

A recent study compared the time spent together by single and dual-earner couples. According to the records kept during the study, the mean amount of time spent together watching TV among single-earner couples was 60 minutes per day, with a standard deviation of 15.5 minutes. For the dual-earner couples, the mean time was 48.4 and the standard deviation was 18.1. At a 0.01 significance level, can we conclude that the single-earner couples on average spend more time watching TV together? There were 12 single-earner and 12 dual-earner couples studied. State the decision rule, the value of the test statistic, and your decision.
A) Reject if t > 2.485, t = 2.77, single-earner couples spend more time watching TV together.
B) Reject if t > 2.508, t = 1.96, insufficient evidence to say that single-earner couples spend more time watching TV together.
C) Reject if t > 2.797, t = 2.57, single-earner couples spend more time watching TV together.
D) Reject if t > 2.508, t = 1.69, insufficient evidence to say that single-earner couples spend more time watching TV together.
E) Reject if t > 2.508, t = 0.96, insufficient evidence to say that single-earner couples spend more time watching TV together.

Quizplus · Accepted Answer

We will perform a two-sample t-test with unequal variances as the standard deviations are different. 
Null hypothesis: The mean time spent watching TV together by single-earner and dual-earner couples is the same.
Alternative hypothesis: The mean time spent watching TV together by single-earner couples is more than dual-earner couples. 
The decision rule for a one-tailed test at a 0.01 significance level with 22 degrees of freedom is t>2.508. 
The test statistic is calculated as:
t = (60 - 48.4) / sqrt[(15.5^2/12) + (18.1^2/12)] = 1.69
The calculated t-value of 1.69 is lesser than the critical value of 2.508. 
Therefore, we fail to reject the null hypothesis and conclude that there is insufficient evidence to say that single-earner couples spend more time watching TV together than dual-earner couples.

A Recent Study Compared the Time Spent Together by Single