Question

According to the website Rotten Tomatoes, the movie “The Peanuts Movie” received 92 critic reviews. Of these 92 reviews, 79 of them were positive reviews (a fresh tomato) and 13 of them were negative reviews (a rotten tomato.) Test the claim made by 20^th Century Fox, the company which made The Peanuts Movie that more than 80% of all critics gave this movie positive reviews. To this end find the following (at alpha = 0.05):

1. State the Null Hypothesis
2. State the Alternative Hypothesis
3. Find the test statistic
4. State the critical value
5. Make conclusions about your hypothesis test
6. Find the P-value for this sample data

Answer 1

The sample size is N = 92, the number of favorable cases is X = 79, and the sample proportion is , and the significance level is α=0.05

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: p = 0.80

Ha:p > 0.80

This corresponds to a right-tailed test, for which a z-test for one population proportion needs to be used.

(2) Rejection Region

The significance level is α=0.05, and the critical value for a right-tailed test is zc​=1.64.

The rejection region for this right-tailed test is R = { z : z > 1.64}

(3) Test Statistics

The z-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that z = 1.407 ≤ zc ​= 1.64, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p = 0.0796, and since p = 0.0796 ≥ 0.05, it is concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population proportion p is greater than p0​, at the α=0.05 significance level.

Therefore, there is not enough evidence to claim that the more than 80% of all critics gave this movie positive reviews.