Question

A university has found over the years that out of all the students who are offered admission, the proportion who accept is 0.70. After a new director of admissions is hired, the university wants to check if the proportion of students accepting has changed significantly. Suppose they offer admission to 1200 students and 888 accept. Is this evidence at the α = .05 level that there has been a real change from the status quo?

Answer 1

This is one sample proportion Z test -
Hypothesis is --
null hypothesis:
alternative hypothesis:

The formula of Z is as follows:

Where,

x = 888, n = 1200
therefore,

using the given values,
z =3.024
Since,The given level of significance == 0.05
Critical value = 1.96(I have used excel to obtain this, command is "=Normsinv(probability), here, probability =0.975)

Decision rule using critical values.

For two tailed one sample proportion Z test :
1) If absolute value of z-test statistic > absolute critical z value then we reject the null hypothesis
2) If absolute value of z-test statistic < absolute critical z value then we fail to reject the null hypothesis
Here |z-test statistic value| =3.024 > |critical z value| =1.96 , So we reject the null hypothesis

Conclusion: We reject the null hypothesis. There is significance evidence to conclude that there has been a real change from the status quo.

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