a. A random sample of senior citizens living in a retirement village reported that they had an average of 1.42 facetoface interactions per day with their neighbors. A random sample of those living in ageintegrated communities reported 1.58 interactions. Is the difference significant?
Sample 1 (Retirement Community) 
Sample 2 (AgeIntegrated Neighborhood) 






b. Senior citizens living in the retirement village reported that they had an average of 7.43 telephone calls with friends and relatives each week, while those in the ageintegrated communities reported an average of 5.50 calls. Is the difference significant?
Sample 1 (Retirement Community) 
Sample 2 (AgeIntegrated Neighborhood) 






(a)
To find:
If the senior citizens who live in retirement communities are more socially active than those who live in age integrated communities.
Given:
The sample statistics is given in the table below,
Sample 1 (Retirement Community) 
Sample 2 (AgeIntegrated Neighborhood) 
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 0
(b)
To find:
If the senior citizens who live in retirement communities are more socially active over the phone than those who live in age integrated communities.
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