As the director of the local Boys 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 non members are gathered and interviewed with respect to their involvement in delinquent activities. Each respondent is asked to enumerate the number of delinquent acts he has engaged in over the past year. The average numbers of admitted acts of delinquency are reported below. What can you tell the funding agency?
Sample 1 (Members) 
Sample 2 (Nonmembers) 






To find:
If the membership in the local boys club reduces juvenile delinquency.
Given:
The sample statistics is given in the table below,
Sample 1 (Members) 
Sample 2 (Nonmembers) 
Approach:
The five step model for hypothesis testing is,
Step 1. Making assumptions and meeting test requirements.
Step 2. Stating the null hypothesis.
Step 3. Selecting the sampling distribution and establishing the critical region.
Step 4. Computing test statistics.
Step 5. Making a decision and interpreting the results of the test.
Formula used:
The formula to calculate the sampling distribution of the differences in sample means of small samples is given by,
Where,
Where,
Calculation:
As the significant difference in the sample statistics is to be determined and a direction has been predicted, a one tailed test is applied.
Follow the steps for twosample testing as,
Step 1. Making assumptions and meeting test requirements.
Model:
Independent random samples.
Level of measurement is interval ratio.
Population Variance is Equal.
Sampling distribution is Normal.
Step 2. Stating the null hypothesis.
The statement of the null hypothesis is that there is no significant difference in the samples of the population. Thus, the null and the alternative hypotheses are,
Step 3. Selecting the sampling distribution and establishing the critical region.
Since, the sample size is small, t distribution can be used.
Thus, the sampling distribution is t distribution.
The level of significance is,
Degrees of freedom is,
Area of critical region is,
Step 4. Computing test statistics.
The population standard deviations are unknown.
The formula to calculate
Substitute 2
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