Question

You wish to test the following claim a significance level of α = 0.005 . H o : p = 0.2 H a : p < 0.2 You obtain a sample of size n = 643 in which there are 119 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 0.2.

There is not sufficient evidence to warrant rejection of the claim that the population proportion is less than 0.2.

The sample data support the claim that the population proportion is less than 0.2.

There is not sufficient sample evidence to support the claim that the population proportion is less than 0.2.

Answer 1

Using TI 84 calculator

press stat then tests then 1-PropZTest

enter the data

po = 0.20

x = 119

n = 643

prop < po

press enter, we get

z statistic = -0.946

p value = 0.1721

it is clear that the p value is greater than significance level of 0.005, so we failed to reject the null hypothesis as the result is not significant

The p-value is... greater than α This test statistic leads to a decision to...

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 0.2. (because the result is insignificant and we failed to reject the null hypothesis)