Question

You wish to test the following claim (H1H1) at a significance level of α=0.05

      Ho:p=0.71
      H1:p≠0.71

You obtain a sample of size n=567 in which there are 394 successful observations.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.71.
• There is not sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.71.
• The sample data support the claim that the population proportion is not equal to 0.71.
• There is not sufficient sample evidence to support the claim that the population proportion is not equal to 0.71.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.71

H_a : p 0.71

= x / n = 394 / 567 = 0.6949

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.6949 - 0.71 / [(0.71 * 0.29) / 567]

= -0.793

P-value = 0.4277

The p-value is greater than α .

Fail to reject the null .

There is not sufficient evidence to warrant rejection of the claim that the population

proportion is not equal to 0.71.