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 64 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 20 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 2.457, t = 2.59, single-earner couples spend more time watching TV together.
B) Reject if t 2.508, t = 0.96, 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 2.042, t = 1.96, insufficient evidence to say that single-earner couples spend more time watching TV together.
E) Reject if t 2.485, t = 2.77, 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 64 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 20 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 > 2.457, t = 2.59, single-earner couples spend more time watching TV together.
B) Reject if t > 2.508, t = 0.96, 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 > 2.042, t = 1.96, insufficient evidence to say that single-earner couples spend more time watching TV together.
E) Reject if t > 2.485, t = 2.77, single-earner couples spend more time watching TV together.

Quizplus · Accepted Answer

The decision rule is to reject if t > 2.457. The calculated t-value is 2.59, which is greater than 2.457, indicating that single-earner couples spend more time watching TV together.

A Recent Study Compared the Time Spent Together by Single