Question

A sample of 30 families in New York showed that those families stay home an average of 35 months with a variance of 90,
while a sample of 25 families in Texas showed an average of 50 months with a variance of 150.
Use the ratio of variances test at α = 0.05 to determine which t-test (pooled variance or separate variance) would be more appropriate for testing the equality of mean length of stay for the two populations of New York and Texas.

1) H0:
Ha:

2) Test statistic:

3) Rejection decision, and why?

4) Conclusion from problem:

Answer 1

NULL HYPOTHESIS H0:

ALTERNATIVE HPOTHESIS Ha:

alpha= 0.05

F= 90/150

F= 0.6

F critical with (30-1=29) and (25-1=24) is 1.94 at 0.05 level of significance

Rejection Region: Reject H0 if F cal>1.94

Fail to reject null hypothesis H0 at 0.05 since calclated value of F is SMALLER than critical value of F .

4) Conclusion: Since we failed to reject null hypothesis we can conclude that variances are equal .We will use t test with pooled variance would be more appropriate for testing the equality of mean length of stay for the two populations of New York and Texas.