Suppose the office of undergraduate education at Penn State is interested in the proportion of undergraduate students who does not meet with their academic advisers at least once during their sophomore year. A study collected responses from 100 randomly sampled PSU undergraduate students of which 23% said they did not meet with their academic advisers at least once during their sophomore year.

If the true proportion was 30% or higher, what is the probability your sample data would produce a sample proportion of 23% or lower?

Be sure to set up the two competing hypotheses and provide a statistical conclusion statement at a 2% level of significance for your results.

Please verify i did this correct:

True proportion = p = 30% =0.3

q = 1-p = 1-0.3 = 0.7

n = sample size = 100

Sample proportion, p hat = 23% = 0.23

The hypothesis for this test is stated as follows;

Ho:P0.3

H1:P<0.3

Note: this is a one tailed test (lower one tailed test)

To test this hypothesis, we use the Z statistic given as;

Z=pq/np^p

Z=1000.30.70.230.30=1.5275

The probability your sample data would produce a sample proportion of 23% or lower is given as;

P(0.23)=P(Z1.5275)=0.0633

At 2% significance level (Alpha = 0.02)

Decision rule;

If the p value is greater than alpha value, we do not reject the null hypothesis

If the p value is less than or equal to the alpha value, reject the null hypothesis.

Since, p value (0.0633) > 0.02, we do not reject the null hypothesis.

Conclusion:

At 2% level of significance, we have enough evidence to conclude that the proportion of undergraduate students who does not meet with their academic advisers at least once during their sophomore year is 30% or higher.

MY QUESTION:

Explain the type II error in the context of the problem.

I also need the uploaded problem in Minitab!