Question

Please explain in written format and EXCEL function.

A statistics instructor believes that fewer than 20% of students at a local college attended the premiere showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 of them attended the midnight showing.

At a 1% level of significance, an appropriate conclusion is

1. insufficient evidence to accept the claim (conclude) that the percentage of students who attended the midnight showing of Harry Potter is less than 20%.
2. insufficient evidence to accept the claim (conclude) that the percentage of students who attended the midnight showing of Harry Potter is more than 20%.
3. sufficient evidence to accept the claim (conclude) that the percentage of students who attended the midnight showing of Harry Potter is less than 20%.
4. insufficient evidence to accept the claim (conclude) that the percentage of students who attended the midnight showing of Harry Potter is at least 20%.

Answer 1

Solution:

The provided information: number of favorable cases = x = 11 and the sample size is n = 84.
So, Sample proportion = x / n = 11 / 84 = 0.131
(1) Null and Alternative Hypotheses:
The following null and alternative hypotheses need to be tested:

Ho: p = 0.2
Ha: p < 0.2
This corresponds to a Left tail test, for which a z-test for one proportion will be used.

(2) Rejection Region:
Given significance level = α = 0.01
So Critical Value for the test is, Zc = -2.33 .....Using excel formula
=NORMSINV(0.01)

(3) Test statistic:

The z-statistic is computed as follows р — Ро 0.131 0.2 -1.582 VPo(1 po)/n V0.2(1-0.2)/84

(4). Decision: Since it is observed that |z| = 1.5821 ≤ Zc = 2.33
It is then concluded that the Null Hypothesis is not rejected.

(5). Conclusion: It is concluded that the Null Hypothesis is not rejected. Therefore, there is not enough evidence to claim that the population proportion p is Less than 0.2, at the 0.01 significance level.

That is, Insufficient evidence to accept the claim (conclude) that the percentage of students who attended the midnight showing of Harry Potter is less than 20%.

Hence option a is correct.

Done