Question

You wish to test the following claim ( H 1 ) at a significance level of α = 0.01 . H o : p = 0.78 H 1 : p > 0.78 You obtain a sample of size n = 453 in which there are 377 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) α

-greater than α

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 greater than 0.78.

-There is not sufficient evidence to warrant rejection of the claim that the population proportion is greater than 0.78.

-The sample data support the claim that the population proportion is greater than 0.78.

-There is not sufficient sample evidence to support the claim that the population proportion is greater than 0.78.

Answer 1

Given,

Hypothesis:

H₀ : p=0.78

H₁: p > 0.78

n = 453

x=377

First calculate sample proportion

p^ =x/n = 377/453 = 0.8322

1) test statistic Z value

z = (p^-p) /((p*(1-p))/n)

= (0.8322-0.78)/((0.78*(1-0.78))/453)

z = 2.682

2) p value for Z test statistic is 0.0036.

P value = 0.0036

3) result:

P value (0.0036) is less than 0.01 level of significance. Hence reject null hypothesis.

4) conclusion:

Reject the null hypothesis. There is sufficient evidence to conclude that the proportion is greater than 0.78.