Question

A researcher wishes to see if there is a difference between the mean number of hours per week that a family with no children participates in recreational activities and a family with children participates in recreational activities. She selects two random samples and the data are shown. Use μ1 for the mean number of families with no children. At =α0.01, is there a difference between the means? Use the P-value method and tables. X σ n No children 8.6 2.6 22 Children 10.1 2.7 22

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ1 = μ2
Alternative Hypothesis, Ha: μ1 ≠ μ2

Rejection Region
This is two tailed test, for α = 0.01
Critical value of z are -2.576 and 2.576.
Hence reject H0 if z < -2.576 or z > 2.576

Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(6.76/22 + 7.29/22)
sp = 0.7991

Test statistic,
z = (x1bar - x2bar)/sp
z = (8.6 - 10.1)/0.7991
z = -1.88

P-value Approach
P-value = 0.0601
As P-value >= 0.01, fail to reject null hypothesis.