Question

Suppose a university advertises that its average class size is 31 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 40 classes was​ selected, and the average class size was found to be 33.1 students. Assume that the standard deviation for class size at the college is 9 students. Using α=0.01​, 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.
H0​: μ ____ (> ≥ = < ≤ ≠).
H1​: μ ____ (= ≤ ≥ < > ≠)
The​ z-test statistic is ____
​(Round to two decimal places as​ needed.)
The critical​ z-score(s) is(are) ____.
​(Round to two decimal places as needed. Use a comma to separate answers as​ needed.)
Because the test statistic _____________ (does not fall within the critical values, is greater than the critical value, is less than the critical value, falls within the critical values)
______(do not reject, reject) the null hypothesis.
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Answer 1

H0​: μ ____ ≤ 31

H1​: μ ____ > 31

The​ z-test statistic is ____ 0.0369

The critical​ z-score(s) is(are) ____ ± 2.33

Because the test statistic _____________ falls within the critical values,

______do not reject, the null hypothesis.

Explanation:

We want to find that the average class size is 31 or less so we set up our hypothesis as

H0​: μ ____ ≤ 31

H1​: μ ____ > 31 One tailed test

Here

Sample size = n= 40

Sample mean = x`= 33.1

Standard Deviation = σ= 9

Level of significance=∝= 0.01

The​ z-test statistic is ____ 0.0369

z= x`- u/σ/√n

z= 33.1-31/9/√40

z= 2.1/56.92099= 0.03689= 0.0369

Z∝ for one tailed test for 0.01 significance level is ± 2.33

The critical​ z-score(s) is(are) ____ ± 2.33

Since the calculated value falls in the acceptance region we accept H0​: μ ≤ 31 and reject alternate hypothesis H1​: μ > 31.

Because the test statistic _____________ falls within the critical values,

______do not reject, the null hypothesis.