Question

In: Statistics and Probability

Suppose a university advertises that its average class size is 30 or less. A student organization...

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

Expert Solution

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.

Please let me know in comments if anything is unclear. Will reply ASAP. Please upvote if satisfied!

orchestra answered 2 years ago

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