A random sample of size n = 10 is taken from a large population. Let µ be the unknown population mean. A test is planned of H0 : µ = 12 vs. HA : µ 6= 12 using α = 0.1. A QQ plot indicates it it is reasonable to assume a normal population. From the sample, ¯x = 14.2 and s = 4.88.

a. Since the data leave it plausible that the population is normal, and the population standard deviation σ is unknown, a t-test is appropriate. Compute the p-value of the test. Do you reject or not reject H0?
b. Compute the power of the test if the true population mean is µA = 15.
c. Using s = 4.88 as our best guess of σ, approximately what sample size would be required to achieve a power of 0.8 if the true population mean is µA = 15? Give your answer as the smallest whole number that meets the criterion.

Find │–14│ a. 14 b. –14 c. start fraction 1 over 14 end fraction

(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?

y=2x−1 5x−4y=1 is (1,1)(1,1) a solution of the system?