Question

The null and alternative hypotheses are:

H0:p1−p2=0H0:p1−p2=0

H1:p1−p2≠0H1:p1−p2≠0

A sample of 340 observations from the first population indicated that X₁ is 300. A sample of 320 observations from the second population revealed X₂ to be 260. Use the 0.02 significance level to test the hypothesis.

a. State the decision rule. (Negative answer should be indicated by a minus sign. Round the final answers to 2 decimal places.)

The decision rule is to reject H₀ if z   is outside  (  ,  ).

b. Compute the pooled proportion. (Round the final answer to 2 decimal places.)

The pooled proportion is  .

c. Compute the value of the test statistic. (Round the final answer to 2 decimal places.)

The test statistic is z =  .

.

e. Determine the p-value. (Round the final answer to 4 decimal places.)

The p-value is  .

Answer 1

The null and alternative hypotheses are:

For sample 1:

N1=340, X1 = 300

= 300/340 = 0.88

For sample 2:

N2=320, X2 = 260

= 260/320 = 0.81

Significance level =0.02

a. Decision rule:

At =0.02 the critical value for a two-tailed test is z_c = +/- 2.33

The decision rule is to reject H₀ if z is outside  ( -2.33 , 2.33 ).

b. The pooled proportion is =

c. Test statistic =

e. p-value = 0.0124

As p-value = 0.0124 < 0.02, we reject the null hypothesis.