As the director of the local Boys and Girls Club, you have claimed for years tha
ID: 3065403 • Letter: A
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
Explanation / Answer
a: The independent variable is the categorical variable denoting whether a boy/girl is a member or non-member of the club.
b: The dependent variable is the no. of delinquent acts a boy/girl did in past years.
c: Since the independent variable is categorical having only two values, 1 if boy/girl is the member of club and 0 if boy/girl is a non-member of the club.
d:The dependent variable(number of delinquent acts) can take any of the 0,1,2,3...
e,f: the null hypothesis will be
H0: Average delinquent acts of members of the club is same as the average delinquent acts of non-members of the club.
The alternative hypothesis will be
H1: Average delinquent acts of members of the club is less than the average delinquent acts of non-members of the club.
The test statistic used it "t" test and the corresponding p-value is 0.0052, which is less than 0.01 thus we reject the null hypothesis and accept the alternative hypothesis " Average delinquent acts of members of the club is less than the average delinquent acts of non-members of the club".
Hope this is helpful.Thank You
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