Question

A hypothesis test was conducted to investigate whether the population proportion of students at a certain college who went to the movie theater last weekend is greater than 0.2. A random sample of 100 students at this college resulted in a test statistic of 2.25. Assuming all conditions for inference were met, which of the following is closest to the pp-value of the test?

A. 0.0061
B. 0.0122
C. 0.0244
D. 0.9756
E. 0.9878

Answer 1

The p-value is the probability of observing the test statistic, or a more extreme value, under the assumption that the null hypothesis is true. With a test statistic of 2.25, the p-value is approximately 0.0122.

Step-by-step explanation:

The p-value is the probability of observing the test statistic, or a more extreme value, under the assumption that the null hypothesis is true. In this case, the null hypothesis is that the population proportion of students who went to the movie theater is 0.2. The test statistic of 2.25 indicates that the sample proportion is 2.25 standard deviations away from the assumed population proportion of 0.2.

To find the p-value, we need to calculate the probability of getting a test statistic of 2.25 or a more extreme value in a standard normal distribution. Using a calculator or a z-table, the p-value is approximately 0.0122, which is closest to option B.

Answer 2

B. 0.0122

Step-by-step explanation:

According to the given data the claim is:

"Proportion of students who went to the movie theater last weekend is greater than 0.2"

Since, the word "greater than" is used in the claim, this claim will be our alternate hypothesis and the hypothesis test will be a one-tailed test i.e. Right tailed test because of the word "greater than".

We are given that the hypothesis test was conducted for a random sample of 100 students and it yielded a z-value of 2.25. We have to find the p-value associated with this z-score

So, we have to find p-value corresponding to z-score of 2.25 and Right Tailed Test. We have to use z-table for this purpose and find the probability of z score being greater than 2.25. From the z-table this value comes out to be:

p-value = 0.0122

Therefore, option B gives the correct answer.