Arecent national survey found that high school students watched an average (mean) of 7.2 movies per month with a population standard deviation of 1.0. the distribution of number of movies watched per month follows the normal distribution. a random sample of 49 college students revealed that the mean number of movies watched last month was 6.5. at the 0.05 significance level, can we conclude that college students watch fewer movies a month than high school students?

1. state the null hypothesis and the alternate hypothesis. a. h0: μ ≥ 7.2; h1: μ < 7.2

b. h0: μ = 7.2; h1: μ ≠ 7.2

c. h0: μ > 7.2; h1: μ = 7.2

d. h0: μ ≤ 7.2; h1: μ > 7.2

2. state the decision rule.

a. reject h1 if z < –1.645

b. reject h0 if z > –1.645

c. reject h1 if z > –1.645

d. reject h0 if z < –1.645

3. compute the value of the test statistic. (negative amount should be indicated by a minus sign. round your answer to 2 decimal places.)

value of the test

(20 points) a bank has been receiving complaints from real estate agents that their customers have been waiting too long for mortgage confirmations. the bank prides itself on its mortgage application process and decides to investigate the claims. the bank manager takes a random sample of 20 customers whose mortgage applications have been processed in the last 6 months and finds the following wait times (in days): 5, 7, 22, 4, 12, 9, 9, 14, 3, 6, 5, 15, 10, 17, 12, 10, 9, 4, 10, 13 assume that the random variable x measures the number of days a customer waits for mortgage processing at this bank, and assume that x is normally distributed. 2a. find the sample mean of this data (x ě…). 2b. find the sample variance of x. find the variance of x ě…. for (c), (d), and (e), use the appropriate t-distribution 2c. find the 90% confidence interval for the population mean (îľ). 2d. test the hypothesis that îľ is equal to 7 at the 95% confidence level. (should you do a one-tailed or two-tailed test here? ) 2e. what is the approximate p-value of this hypothesis?