Question

Suppose a university advertises that its average class size is 30 or less. A student organization is concerned that budget cuts have led to increased class sizes and would like to test this claim. A random sample of 39 classes was​ selected, and the average class size was found to be 32.8 students. Assume that the standard deviation for class size at the college is 7 students. Using alpha equals 0.05​, complete parts a and b below. a. Does the student organization have enough evidence to refute the​ college's claim? Determine the null and alternative hypotheses. Upper H 0​: mu ▼ less than or equals less than greater than not equals equals greater than or equals nothing Upper H 1​: mu ▼ not equals greater than less than less than or equals greater than or equals equals nothing

b) Determine the p value for this test

c) verify your result using PHstat

Answer 1

The provided sample mean is and the known population standard deviation is , and the sample size is n=39.

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ≤30

Ha: μ>30

This corresponds to a right-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

Test Statistics

The z-statistic is computed as follows:

The p-value is p = 0.0062

Decision about the null hypothesis

Since it is observed that z=2.498>zc​=1.64, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0.0062, and since p=0.0062<0.05, it is concluded that the null hypothesis is rejected.

Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is greater than 30, at the 0.05 significance level. Hence the student organisation concerns are well founded.

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