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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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.

Step-by-step 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.

first, you divide the triangle in two, tô form a retangle triangle. after, using pythagoream theorem:

18^2 = 14^2 + (x/2)^2

(x^2/4) + 196 = 324

x^2/4 = 324 - 196

x^2/4 = 128

x^2 = 512

x = √512

x = √2^9

x = 16√2 cm

i hope i you.