Variable  Freshmen  All Students  
a.  Proportion Republican 


b.  Proportion majoring in math and science 


c.  Average family income 


d.  Average number of siblings 


e.  Average number of telephone calls to parents per week 


f.  Average number of close friends living on campus 


a)
To find:
The significant difference between the given statements.
Given:
The given information is,
A researcher is studying changes in the student body at her university and has selected a random sample of 163 from the freshman class.
The given table of information is,
Variable  Freshmen  All Students  
a.  Proportion Republican 
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:
For large samples with single sample proportions, the Z value is given by,
Where,
N is the sample size.
Calculation:
From the given information, the sample size is 163, sample proportion is
Follow the steps for twotailed hypothesis testing as,
Step 1. Making assumptions and meeting test requirements.
Model:
Random sampling.
Level of measurement is interval ratio.
Sampling distribution is Normal.
Step 2. Stating the null hypothesis.
The statement of the null hypothesis is that the proportion of republican from the sample of freshmen is not significantly different from all the students.
Thus, the null and the alternative hypotheses are,
Step 3. Selecting the sampling distribution and establishing the critical region.
Since, the sample is large, Z distribution can be used.
The information given is in the form of proportions, the test for proportion can be used.
Thus, the sampling distribution is Z distribution
b)
To find:
The significant difference between the given statements.
c)
To find:
The significant difference between the given statements.
d)
To find:
The significant difference between the given statements.
e)
To find:
The significant difference between the given statements.
f)
To find:
The significant difference between the given statements.
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