QUESTION 1

1. A user survey is completed by 35 individuals testing a new interface. They each score the interface on a 1 to 100 scale. The average score is 71 with a standard deviation of 4. The designer wants to test the hypothesis that the rating is above 70 with 95% confidence. Which of these is the appropriate null hypothesis? (Ho: ? < 70 , Ho: ? ? 70 , Ho: ? < 72, or Ho: ? ? 72) What z-value is calculated as the test statistic for this hypothesis? What is the p-value associated with this z? What is the decision? (fail to reject null hypothesis , reject null hypothesis) With 95% confidence, is the mean greater than 70? 8 points QUESTION 2 1. A programmer has developed a random number generator that gives a normally distributed set of results based on an input population mean and population standard deviation. To test the program, he inputs a mean of 20 and a standard deviation of 5. He generates 14 random numbers with a sample mean of 21.7 and a sample deviation of 5. He wants to test with 95% confidence whether or not this sample has the correct mean of 20. Which of these is the appropriate null hypothesis? (Ho: ? = 20 or Ho: ? =21.7) What z-value is calculated as the test statistic for this hypothesis? What is the p-value associated with this z? What is the decision? (fail to reject null hypothesis or reject null hypothesis) With 95% confidence based on this measurement, is the program working correctly? (yes or no) 8 points QUESTION 3 1. A performance specification requires a variance of less than 0.20 (?2?0.20). A sample of 15 batches have an average variance of 0.23 (s2=0.23). For a 90% confidence, is this sample out of spec? Which of these is the appropriate null hypothesis? (Ho: ? = 0.20 , Ho: ? =0.23, Ho: ?2 = 0.20 or Ho: ?2 =0.23) What is the chi-squared (?2) cut-off value for rejecting the null hypothesis given n=15 and ?=0.10? What ?2-value is calculated as the sample statistic for this hypothesis? What is the decision? (fail to reject null hypothesis or reject null hypothesis) With 95% confidence based on this measurement, do these batches need to investigated for not meeting the variance spec? 8 points QUESTION 4 1. The table below gives process times for two different systems running a series of computation tasks. A system administrator wishes to utilize a t-test with 95% confidence to assess whether or not the two systems perform differently. Test A Test B Test C Test D Test E System Alpha 45 92 21 33 74 System Beta 56 86 24 42 80 2. Are these samples independent, dependent, or paired? a. independent b. dependent c. paired 2 points QUESTION 5 1. Fill in the remaining values in the difference table: Test A Test B Test C Test D Test E Beta-Alpha Difference 11 9 3 points QUESTION 6 1. What is the t-statistic value for this test? 1 points QUESTION 7 1. What is the average difference? 1 points QUESTION 8 1. What is the standard deviation of the difference? 1 points QUESTION 9 1. What are the bounds of the 95% confidence interval for difference with values to the nearest tenth: _ ____? d ? _ ____. 2 points QUESTION 10 1. Based on this analysis, is there a significant difference between System Alpha and System Beta? a. yes b. no 1 points QUESTION 11 1. If testing the null hypothesis d=0 at 95% confidence, what is the resulting conclusion? a. fail to reject null hypothesis b. reject null hypothesis 1 points QUESTION 12 1. A hypothesis test wishes to assess the difference between two means for independent samples. Which equation gives the correct calculation for t for this test? Operating System Equation A Equation B Equation C Equation D