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? There were 15 single-earner and 12 dual-earner couples studied. Hint: For the calculations, assume the single-earner as the first sample.

a. State the decision rule for 0.01 significance level: H₀: μ_s – μ_d ≤ 0;H₁: μ_s –μ_d > 0. (Round the final answer to 3 decimal places.)

The decision rule is to reject H₀ if t is greater than  Correct2.485 2.485 Correct .

This is a one  Correct-tailed test.

b. Compute the pooled estimate of the population variance. (Round the final answer to 2 decimal places.)

Pooled estimate of the population variance            278.69 278.69 Correct

c. Compute the value of the test statistic. (Round the final answer to 3 decimal places.)

Value of the test statistic            1.949 1.949 Correct

d. What is your decision regarding H₀?

Do not reject  CorrectH₀.

e. Calculate the p-value. (Round the final answer to 4 decimal places.)

The p-value is __________

Answer 1

Solution:-

From the given information, there is Right-tailed test

Here, n1=15, n2= 12

Degrees of freedom for pooled t-test is ,

df=n1+n2-2=15+12-2=25

Null and Alternative hypothesis is,

H0: μs – μd ≤ 0

H1: μs – μd > 0

Pooled t-test statistics is,

t=1.949

Now, with df=25,

P-value=P(t>t=1.949)

P-value=0.0313

Here,

P-value>

Do not reject H0.