The official release date of Star Wars: The Rise of Skywalker was Friday, De- cember 20, 2019

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The official release date of Star Wars: The Rise of Skywalker was Friday, De- cember 20, 2019. However, many theaters around the world screened the movie on the preceding Thursday night. A cultural anthropologist studying our engagement with popular culture believes that 4% of all US adults made plans to see the new Star Wars movie on the Thursday night. She collected a random sample of n = 1820 US adults, independently sampled. Let X be the number of individuals in the sample who saw the latest Star Wars movie on Thursday, December 19th.

1. What is the distribution of X? Identify and write down all relevant parameters.
2. Suggest a distribution that can be used to approximate X. Check any conditions necessary for the approximation to hold.
3. Use the approximate to calculate the probability that than 66 or more individuals in the sample have tickets. For statistics assignment
4. After collecting the data, the researcher observes that 111 individuals in the observed sample have tickets. Use this information to test the null hypothesis H0 : p = 0.04 against an alternative that the true proportion is greater than 0.04 at the 5% level of significance. Clearly state your conclusion for this hypothesis test, showing all supporting calculations. Your conclusion may be based on the calculation of either a p-value or a confidence interval.
5. Assume that the alternative hypothesis is true with p′ = 0.07. Calculate the sample size needed for the hypothesis test described in (d) to have type II error probability β = 0.05 at the significance level α = 0.05.