You receive a brochure from a large university. The brochure indicates that the

Question

You receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is fewer than 33 students. You want to last this claim. You randomly select 18 classes taught by full-time faculty and determine the class size of each. The results are shown in the table below. At alpha = 0.05, can you support the university's claim? complete parts (a) through (d) below. Assume the population is normally distributed. Write the claim mathematically and identify H_0 and H_a. Which of the following correctly states H_0 and H_a Use technology to find the P-value. (Round to three decimal places as needed.) Decide whether to reject or fail to reject the null hypothesis. Which of the following is correct? Fail to reject H_0 because the P-value is less than the significance level. Reject H_0 because the P-value is less than the significance level. Reject H_0 because the P-value is greater than the significance level. Fail to reject H_0 because the P-value is greater than the significance level. Interpret the decision in the context of the original claim. At the 5% level of significance, there is not sufficient evidence to support the claim that the mean class size for full-time faculty is fewer than 33 students. At the 5% level of significance, there is sufficient evidence to support the claim that the mean class size for full-time faculty is fewer than 33 students. At the 5% level of significance, there is not sufficient evidence to support the claim that the mean class size for full-time faculty is more than 33 students. At the 5% lvevel of significance, there is sufficient evidence to support the claim that the mean class size for full-time faculty is more than 33 students.

Explanation / Answer

The null hypothesis is mean strength is less than 33

So,

Ho : mean < 33

Ha : Mean >= 33

Now,

Sample mean = 30.22

SD = 4.346

p- value = 0.0033

So, we fail to reject the null hypothesis since the p-value is less than the significance level

Hence, it can be stated that the mean class size is indeed less than 33 students.

Hope this helps.

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