Question

You wish to test the claim that the population proportion is not equal to 0.73 at a significance level of α=0.10α=0.10.

You obtain a sample of size 156 in which there are 106 successful observations.

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value = ±±

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

The test statistic is...

• in the critical region
• not in the critical region

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 0.73.
• There is not sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.73.
• The sample data support the claim that the population proportion is not equal to 0.73.
• There is not sufficient sample evidence to support the claim that the population proportion is not equal to 0.73.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.73

Ha : p 0.73

n = 156

x = 106

= x / n = 106 / 156 = 0.68

P0 = 0.73

1 - P0 = 1 - 0.73 =0.27

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.68 - 0.73 / [(0.73*0.27) / 156]

= -1.42

Test statistic = z = -1.42

The critical value = -1.645 and 1.645

P(z < -1.42) = 0.0778

P-value = 0.0778

= 0.10

P-value <

0.0778 < 0.10

Reject the null hypothesis .

There is sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.73.