Question

You wish to test the following claim a significance level of α = 0.05 . H o : p = 0.24 H a : p < 0.24 You obtain a sample of size n = 160 in which there are 26 successful observations. What is the test statistic for this sample? test statistic = Round to 3 decimal places. What is the p-value for this sample? P-value = Use Technology Round to 4 decimal places. 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 less than 0.24. There is not sufficient evidence to warrant rejection of the claim that the population proportion is less than 0.24. The sample data support the claim that the population proportion is less than 0.24. There is not sufficient sample evidence to support the claim that the population proportion is less than 0.24.

Answer 1

(a)

Question: What is the test statistic for this sample?

n = Sample Size

= Sample Proportion = 26/160 = 0.1625

p = Population Proportion = 0.24

q = 1 - p = 0.76

SE =

Test Statistic is given by:

Z = (0.1625 - 0.24)/0.0338

= - 2.293

So,

test statistic = - 2.293

(b)

By Technology, P - Value = 0.0109

(c)

The p-value is 0.0109 less than (or equal to) α

This test statistic leads to a decision 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 less than 0.24.