Question

A random sample of households in Orange County showed that 11 out of 162 them were burglarized in the past 5 years. And in a random sample of households in Cook County, 25 out of 238 of them were burglarized in that same time period. We will test the claim that the proportion of Orange County households that were burglarized (p1) is not equal to the proportion of Cook County households that were burglarized (p2). For each part below, enter only a numeric value in the answer box. For example, do not type "z =" or "t =" before your answers. Round each of your answers to 3 places after the decimal point.

(a) Calculate the value of p¯ , the pooled sample proportion, that is used in this hypothesis test. p¯ =

(b) Calculate the value of the test statistic used in this test. Test statistic's value =

(c) Use your calculator to find the P-value of this test. P-value =

(d) Use your calculator to find the critical value(s) used to test this claim at the 0.06 significance level. If there are two critical values, then list them both with a comma between them. Critical value(s) =

Answer 1

(a)

(b)

Test Statistic is

(c)

Table of Area Under Standard Normal Curve gives area = 0.3980

So,

P - Value = (0.5 - 0.3980) X 2 = 0.204

(d)

= 0.06

From calculator, critical values of Z = 1.881

So,

Critical values: - 1.881, 1.881

Since calculated value of Z = - 1.274 is greater than critical value of Z =- 1.881, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim that the proportion of Orange County households that were burglarized (p1) is not equal to the proportion of Cook County households that were burglarized (p2).