A movie production company is releasing a movie with the hopes of many viewers returning to see the movie in the theater for a second time. Their target is to have 30 million viewers, and they want more than 30% of the viewers to return to see the movie again. They show the movie to a test audience of 200 people, and after the movie they asked them if they would see the movie in theaters again. Of the test audience, 68 people said they would see the movie again. (You may find it useful to reference the appropriate table: z table or t table)

a. Specify the competing hypotheses to test if more than 30% of the viewers will return to see the movie again.

• H₀: p = 0.30; H_A: p 0.30
• H₀: p 0.30; H_A: p < 0.30
• H₀: p 0.30; H_A: p > 0.30

b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

Test Statistic

b-2. Find the p-value.

• p-value 0.01
• 0.01 < p-value 0.025
• 0.025 < p-value 0.05
• 0.05 < p-value 0.10
• p-value > 0.10

c. At the 5% significance level, what is the conclusion?

• Reject H₀, the population proportion is greater than 0.30.
• Reject H₀, the population proportion is not greater than 0.30.
• Do not reject H₀, the population proportion is greater than 0.30.
• Do not reject H₀, the population proportion is not greater than 0.30.

d. Repeat the analysis at a 10% level of significance.

• Reject H₀
• Do not reject H₀

e. Interpret your results.

The production company's expectations of more then 30% of viewers returning to the theaters for the same movie is__________ by the sample data.