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 0.01 significance level, can we conclude that the single-earner couples on average spend more time watching television together?

Answer 1

Answer:

There is evidence to show that  the single-earner couples on average spend more time watching television together

Step-by-step explanation:

Given that 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.

$H_0: \bar x=\bar y\\H_a: \bar x > \bar y$

(Right tailed test where x stands for single earner and y for double)

Let us assume sample sizes are 500 each.

Difference -12.600

Standard error 1.066

95% CI -14.6913 to -10.5087

t-statistic  -11.823

DF  998

Significance level P < 0.0001

Since p is less than alpha we reject null hypothesis.

There is evidence to show that  the single-earner couples on average spend more time watching television together