Question

As the director of the local Boys and Girls Club, you have claimed for years that membership in your club reduces juvenile delinquency. Now, a cynical member of your funding agency has demanded proof of your claim. Random samples of members and nonmembers are gathered and interviewed with respect to their involvement in delinquent activities. Each respondent is asked to enumerate the number of delinquent acts he/she has engaged in over the past year. The average number of admitted acts of delinquency are reported below. What can you tell the funding agency? Use an alpha of .01.

First, identify your (a) independent and (b) dependent variables.

Second, identify the (c) level of measurement for your independent variable and (d) the level of measurement for your dependent variable.

Third, (e) list out the steps of the 6 step traditional hypothesis test.

Fourth, (f) run a 6 step traditional hypothesis test.

(Conduct a 6 step traditional hypothesis test, find the p value).

	Members	Non-Members
Mean	10.3	12.3
Standard Deviation	2.7	4.2
Sample Size	40	55

Answer 1

(a) Independent variable is the number of respondents because the number of respondents is not dependent on any thing.

(b) Dependent variable is the number of admitted acts of delinquency because the admitted acts of delinquency is dependent on the response given by the respondents.

(c) level of measurement is 0.01 significance level for the independent variable

(d) level of measurement is 0.01 significance level for the dependent variable

(e) STEP of traditional hypothests tests are

(i) Hypothesis statement

(ii) statistical test selection

(iii) significance level selection

(iv) Defining rejection regions

(v) test statistic calulation

(vi) Conclusion

(f) Running a 6 step traditional hypothesis test

let sample 1 and sample 2 represents group of members and non-members

(i) Hypothesis statement

Claim is that the membership in club reduces the juvenile delinquency, so this will be the alternate hypothesis statement

Null hypothesis (Mean of both groups is same)

Alternate hypothesis (mean of members is less than mean of non-members)   

(ii) statistical test selection

Population variance is unknown, so we will use the t test for the hypothesis.(t-test for comparison of two independent means)

(iii) significance level selection

Significance level is already given in the question, So we will use 0.01 significance level for the hypothesis testing.

(iv) Defining rejection regions

Reject null hypothesis if the calculated p value is less than 0.01 significance level.

(v) test statistic calulation

Formula for the test statistic is given as

t statistic =

where

setting the given values in the above formula for the test statistic, we get

t statistic =

Degree of freedom = n1-1 = 40-1 = 39 (For degree of freedom, either n1 or n2 is selected based on the smaller value)

Using the student's t distribution with degree of freedom 39 and t value = -2.82 for one tailed hypothesis, we get the following p value

p value = 0.0038, it is less than 0.01. So the result is significant.

(vi) Conclusion

The calculated p value is significant at 0.01 significance level, thus we will reject the null hypothesis. We can conclude that we have sufficient evidence to support the claim that the membership in the club reduces juvenile delinquency.