Question

Listed below are 15 lengths (in minutes) of randomly selected movies (R- or PG-rated) that made at least $100 million in gross revenue:

110 119 105 120 144 160 132 150 117 106 127 140 124 150 136

This problem may need more space to answer each question than the space provided. Use the back of the page or attach extra sheets as necessary.

a) Is it possible to apply a confidence interval to estimate the mean length of all R- or PG-rated movies made at least 100 million in gross revenue? Explain why or why not. Then if yes, you answer questions

b) – d). If not, you may leave questions b) – d) blank.

b) Construct a 95% confidence interval estimate of the mean length of all R- or PG-rated movies.

c) One of the movie producers believes that the mean length of all blockbuster movies has to be 120 minutes or longer. Is there sufficient evidence to support the producer’s claim?

d) Assuming that it takes 30 minutes to empty a theater after movie, clean it, all time for the next audience to enter, and show previews, what is the minimum time that a theater manager should plan between start times of movies, assuming that this time will be sufficient for a typical movie?

Answer 1

a) Yes it is possible. Once we construct the confidence interval and if we find the range of all values we can say with 95% confidence that the true mean length lies within that range.

b) 95% confidence interval is,

Sample mean +- t 0.025, n-1 * sample s.d/√n

= 129.333 +- 2.145*17.041/√15

= (119.895, 138.771)

c) Yes there is sufficient evidence to support the claim since we can see that all the values from the above interval Suggest that the mean length >120