For each problem, test the sample proportions for the significance of the difference.
a.
Sample 1  Sample 2 




b.
Sample 1  Sample 2 




(a)
To find:
The significant difference between two sample proportions.
Given:
The sample statistics is given in the table below,
Sample 1  Sample 2 
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 proportions of large samples is given by,
Where,
Where,
And
Calculation:
As the significant difference in the sample proportions is to be determined, a two 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 nominal.
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 large, Z distribution can be used.
Thus, the sampling distribution is Z distribution.
The level of significance is,
Area of critical region is,
Step 4. Computing test statistics.
The population standard deviations are unknown.
The formula to calculate
Substitute 0.20 for
(b)
To find:
The significant difference between two sample proportions.
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