Aresearcher would like to know whether there is a consistent, predictable relationship

between verbal skills and math skills for high school students. a sample of 200 students

is obtained, and each student is given a standardized english test and a standardized math

test. based on the test results, students are classified as high or low for verbal skills and

math skills. the results are summarized in the following frequency distribution:

verbal skills

high low

59

41

31

69

high math 100

low math 100

90 110 n = 200

a. based on the results, can the researcher conclude that there is a significant relationship between verbal skills and math skills? test at the α=.05 level of significance.

b. compute the phi-coefficient to measure the strength of the relationship.

(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?