A corrections researcher wants to see if the likelihood of an arrestee making ba

Question

A corrections researcher wants to see if the likelihood of an arrestee making bail differs by gender. In a random sample of 20 arrestees who were men, 9 made bail. In a random sample of 20 arrestees who were women, 15 made bail. We are going to test H_0: p_w = p_m against H_A: p_w notequalto p_m using significance level alpha = 10, but we are going to conduct the hypothesis test using a confidence interval. (a) If the significance level is alpha = 10, what is the appropriate confidence level for the interval? (b) Using StatKey, find the appropriate confidence interval for p_w - p_m (or p_m - p_w). Copy screenshots of the bootstrap dotplot (with at least 5000 bootstrap samples) and original sample box into your assignment. (c) Is there enough evidence to reject H_0 at significance level alpha = 10? Why or why not? (d) Based on the interval in part b and/or the decision in part c, what must be true about the p-value?

Explanation / Answer

Here we want to test that

So null hypothesis is H0 : Pw = Pm   that is Pw - Pm = 0

and alternative hypothesis is H1 : Pw not equal to Pm

We can used two sample proportion z test.

level of significance = 0.10

Using minitab.

The command for two sample proportion z test in minitab is

Choose Stat > Basic Statistics > 2 Proportions.

Choose Summarized data.

In First sample, under Events, enter . Under Trials, enter .

In Second sample, under Events, enter . Under Trials, enter .

Click on "Option"

Level of confidence in percentage = c = ( 1- lpha)*100 = = (1 -0.1)*100 = 90.0

so put "Confidence level " = 90.0

Test Difference

Alternative = Not equal

Then click on OK and again click on OK

So we get the following output

Test and CI for Two Proportions

Method

Descriptive Statistics

Estimation for Difference

CI based on normal approximation

Test

Decision rule:

1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0.042 < 0.10 so we used first rule.

That is we reject null hypothesis

Conclusion: At 0.10 level of significance there are not sufficient evidence to say that the proportion of sample data of an arrestee making bail is same.

p: proportion where Sample 1 = Event p: proportion where Sample 2 = Event Difference: p - p

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