In the twentieth century, it was a common practice in Southern California for houses to be built with pools in the backyard. For new homes, however, that practice may be changing, possibly as a measure to help reduce climate change. A recent study examined a random sample of 132 houses built in Southern California in the twentieth century and an independent, random sample of 88 new houses built in Southern California. The sample of twentieth century houses contained 76 houses with pools, and the sample of new houses contained 34 houses with pools.Based on this survey, can we conclude, at the 0.01 level of significance, that the proportion p1 of all Southern California twentieth century houses that were built with pools is greater than the proportion p2 of all new Southern California houses that were built with pools? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the parts below. (If necessary, consult a list of formulas.) (For z test statistics) every expert has gotten the z test statistic wrong thus far. I have included pictures of a sample problem and formula. A. State the null hypothesis H0 and the alternative hypothesis H1 B. Find the value of the test statistic. (Round to three or more decimal places.) C. Find the p-value. (Round to three or more decimal places.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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In the twentieth century, it was a common practice in Southern California for houses to be built with pools in the backyard. For new homes, however, that practice may be changing, possibly as a measure to help reduce climate change. A recent study examined a random sample of 132 houses built in Southern California in the twentieth century and an independent, random sample of 88 new houses built in Southern California. The sample of twentieth century houses contained 76 houses with pools, and the sample of new houses contained 34 houses with pools.Based on this survey, can we conclude, at the 0.01 level of significance, that the proportion p1 of all Southern California twentieth century houses that were built with pools is greater than the proportion p2 of all new Southern California houses that were built with pools? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the parts below. (If necessary, consult a list of formulas.)

(For z test statistics) every expert has gotten the z test statistic wrong thus far. I have included pictures of a sample problem and formula.

A. State the null hypothesis H0 and the alternative hypothesis H1

B. Find the value of the test statistic. (Round to three or more decimal places.)

C. Find the p-value. (Round to three or more decimal places.)   

 

   

 

(c) Finding the value of the test statistic
The value of this test statistic is the z-value corresponding to the sample proportion under the assumption that His true. Here is i
P-P
p(1-p)
n
36
43
0.80
0.80(1-0.80)
215
1.364
Transcribed Image Text:(c) Finding the value of the test statistic The value of this test statistic is the z-value corresponding to the sample proportion under the assumption that His true. Here is i P-P p(1-p) n 36 43 0.80 0.80(1-0.80) 215 1.364
A marriage counselor has traditionally seen that the proportion p of all married couples for whom her communication program can prevent divorce is 80%.
After making some recent changes, the marriage counselor now claims that her program can prevent divorce in more than 80% of married couples. In a
random sample of 215 married couples who completed her program, 180 of them stayed together. Based on this sample, is there enough evidence to support
the marriage counselor's claim at the 0.05 level of significance?
Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)
Transcribed Image Text:A marriage counselor has traditionally seen that the proportion p of all married couples for whom her communication program can prevent divorce is 80%. After making some recent changes, the marriage counselor now claims that her program can prevent divorce in more than 80% of married couples. In a random sample of 215 married couples who completed her program, 180 of them stayed together. Based on this sample, is there enough evidence to support the marriage counselor's claim at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)
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