Arandom sample of 160 car crashes are selected and categorized by age. the results are listed below. the age distribution of drivers for the given categories is 18% for the under 26 group, 39% for the 26-45 group, 31% for the 45-65 group, and 12% for the group over 65. calculate the chi-square test statistic
χ to test the claim that all ages have crash rates proportional to their driving rates.
1. under 26 = 66 drivers
2. 26-45 = 39 drivers
3. 46-65 = 25 drivers
4. over 65 = 30 drivers

(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?