# ) Using any method you like, construct a 95% confidence interval for the mean run time of movies.

Part 1 – Mean

1) One is curious how long the average movie really is.

a) Using any method you like, construct a 95% confidence interval for the mean run time of movies.

b) How do you interpret your results?

2) Movie critics claim that ratings are actually artificially inflated. The ratings in the data frame are based on a scale of 0 to 10. If the system is unbiased the mean rating should be around 5. Test whether or not there is significant evidence in the data to believe the population mean rating is different than 5.

a) State the two hypotheses to be tested.

b) Compute the mean rating and the standard deviation of the rating.

c) Determine if there is significant evident that the mean rating is different than 5.

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Part 2 – One Proportion

1) You are interested in determining the percentage of movies that are classified as action movies

a) Compute the proportion of films in your sample that are action movies.

b) Construct a 95% confidence interval for the population proportion

c) How do you interpret your results?

d) Construct a 90% confidence interval.

e) How is the new interval different than the old? Explain both because of the mathematics, but also notionally (e.g. how is 90% confidence different that 95% and how does that affect results.

2) A producer claims that the percentage of movies that lose money is less than 30%.

a) Create a new variable called profit which is revenue minus budget. Use this to count the percentage of movies that lost money.

b) Restate the producer’s claim in terms of a null and alternative hypothesis.

c) Use the Profit variable to compute the sample proportion

d) At a 5% significance level is there evidence to support the producer’s claim?

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Part 3 – Two Means

A person is wondering if Action movies have a higher mean revenue that Comedies Conduct a test to see if the data supports the claim that the mean box office for Action movies is greater than those that are Comedies.

1) State the hypotheses to be tested.

2) Compute the sample means and sample standard deviations for each set of movies.

3) At a 5% significance level, is there evidence to believe the mean for Action films is greater?

4) Are there any concerns about the test? .

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Part 4 – Two Proportions

The film industry has been accused of being biased against female directors. We are going to test whether the proportion of female director directing high budget films is different than other.

1) Compute the proportion of films directed by people who identify as female that has a budget over 10,000,000 and the proportion of films directed by people who do not identify as female that has a budget over 10,000,000.

2) Determine if there is significant evidence that there is a difference in proportions.

3) Any concerns about the data?

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Part 5 – Variance

An executive director claims that his film did not lose a lot of money relatively speaking because the standard deviation of film revenue is \$180,000,000. You believe it might be different than that.

1) State the hypotheses you are testing.

2) Conduct a test to determine if your sample variance is significantly different than the executive director’s number and you can refute their claim.

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