Question

A private and a public university are located in the same city. For the private university, 1038 alumni were surveyed and 647 said that they attended at least one class reunion. For the public university, 808 out of 1311 sampled alumni claimed they have attended at least one class reunion. Is the difference in the sample proportions statistically significant? (Use α=0.0

Answer 1

Answer:

The difference in the sample proportions is not statistically significant at 0.05 significance level.

Step-by-step explanation:

Significance level is missing, it is  α=0.05

Let p(public) be the proportion of alumni of the public university who attended at least one class reunion  

p(private) be the proportion of alumni of the private university who attended at least one class reunion  

Hypotheses are:

$H_{0}$: p(public) = p(private)

$H_{a}$: p(public) ≠ p(private)

The formula for the test statistic is given as:

z=$\frac{p1-p2}{\sqrt{{p*(1-p)*(\frac{1}{n1} +\frac{1}{n2}) }}}$ where

• p1 is the sample proportion of  public university students who attended at least one class reunion  ($\frac{808}{1311}=0.616$)

• p2 is the sample proportion of private university students who attended at least one class reunion  ($\frac{647}{1038}=0.623$)

• p is the pool proportion of p1 and p2 ($\frac{808+647}{1311+1038}=0.619$)

• n1 is the sample size of the alumni from public university (1311)

• n2 is the sample size of the students from private university (1038)

Then z=$\frac{0.616-0.623}{\sqrt{{0.619*0.381*(\frac{1}{1311} +\frac{1}{1038}) }}}$ =-0.207

Since p-value of the test statistic is 0.836>0.05 we fail to reject the null hypothesis.