If t test statistic what are the degrees of freedom? For several decades, it was

Question

If t test statistic what are the degrees of freedom?

For several decades, it was a common practice in Southern California for houses to be built with pools in the backyard (as any airplane flight which ends at a Southern California airport will reveal). Now, however, that practice may be changing, possibly because of the recent demand for landscaped homes, which experts believe help reduce pollution. A recent study examined a random sample of 165 houses built in Southern California between 1950 and 1985 and an independent, random sample of 94 houses built in Southern California from 1992 to the present. The sample of houses built in 1950-1985 contained 65 houses with pools, and the sample of houses built from 1992-present contained 27 houses with pools. Based on this survey, can we conclude, at the 0.1 level of significance, that the proportion p of all Southern California houses built in 1950-1985 that were built with pools is greater than the proportion p2 of all Southern California houses built from 1992-present that were built with pools? Perform a one-tailed test. Then fill in the table below Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) The null hypothesis: The alternative hypothesis:H The type of test statistic: (Choose one) The value of the test statistic: (Round to at least three decimal places.) The critical value at the 0.1 level of significance (Round to at least three decimal places.) Can we conclude that the proportion of Southern California houses built with pools from 1950-1985 is greater than the proportion from 1985-present? Yes No

Explanation / Answer

The statistical software output for this problem is:

Two sample proportion summary hypothesis test:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
H0 : p1 - p2 = 0
HA : p1 - p2 > 0

Hypothesis test results:

Hence,

Ho: p1 - p2< 0

H1: p1 - p2 > 0

Type of test statistic: z

Test statistic = 2.110

Critical value = 1.282

Yes

Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value p1 - p2 94 165 27 65 0.15431235 0.073121209 2.1103638 0.0174

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