Quiz 1 Sections 7.1-7.2 Name ANSWER KEYStat 2171. A study is being conducted to determine whether drivers at or over the age of 70 have longer reaction times in a simple driving task than drivers aged less than 70. A SRS of 10 drivers at or over age 70, and another SRS of 11 drivers under age 70 is selected. Each driver’s reaction time to a specific driving activity was measured in a laboratory, and the reaction times in seconds were recorded. (a) Do we need to assume that the data for each group of drivers must be normal? Why or why not?(1 pt) You can argue either yes or no, as long as you mention that it is the sample size that determines whether or not we need to assume that the data for each group is normal. According to p.533 of your textbook, since 152121 nn, and assuming that there are no outliers, then t-tests are appropriate, and we do not need to assume that the data for each age group are normal, (Recall that in order for1x and 2x to be approximately normal so that t-tests are valid, we need a sufficiently large sample size.)(b) Should you use a pooled or an unpooled procedure for these data?Since s1 = .1020 is close to s2 = .0847, then it appears safe to assume that the population standard deviations are the same, 1 = 2. , and so a POOLED procedure is appropriate. However, to be conservative, you can always use a UNPOOLED test, especially if you believe that the population standard deviations are not the same, 1 is not equal to 2(c) Calculate a 90% C.I. for the true difference in reaction times.(2 pts) Using a POOLED variance estimate, the confidence interval is)1185,.0225.()4369)(.0933(.729.10480.11110119)1020(.9)0847(.10729.1)7140.7620(.22Using an UNPOOLED variance estimate, the confidence interval is)1228,.0267.()0408(.833.10480.110847.101020.833.1)7140.7620(.22(d) Interpret the 90% C.I. in terms of this problem.(1 pt) I am 90% confident that the true mean difference in reaction times for drivers age 70 and above and drivers under 70 is between -.0225 seconds and .1185 seconds. Notice that we can not say which group of drivers has a larger mean reaction time since ZERO is in the confidence interval.2. Test to see if the drivers aged over 70 have a significantly greater mean reaction time.  State the hypotheses. (1 pt) 21210::aHH or 0:0:21210aHH where population 1 is the drivers at or over age 70 and population 2 is the drivers under 70 Calculate the test statistic. SampleMeanSample StandardDeviationAge 70 or over: 0.7620 s. 0.1020 Age under 70: 0.7140 s. 0.0847(1 pt) Using a POOLED t test statistic is1. 1775)43 69(.0933.)7140.7620(.11110119)1020(.9)0847(.10)7140.7620(.22tUsing an UNPOOLED t test statistic is1.17700408.)7140.7620(.110847.101020.)7140.7620(.22t What is the distribution of the test statistic?(1 pt) The (approximate) distribution of the POOLED test statistic is t(19). The (approximate) distribution of the UNPOOLED test statistic is t(9).  Calculate the p-value. (1 pt) Using a t(19) distribution, the p-value is between 10% and 15%, 15.10.  valuep. Usinga t(9) distribution, the p-value is between 10% and 15%, 15.10.  valuep. Make a decision at =0.05. (1 pt) Since the p-value>.10 >.05=, then we FAIL TO REJECT H0.  Make a conclusion in terms of this problem.(1 pt) There is insufficient evidence to suggest that the true mean reaction time for drivers age 70 and above is larger than the mean reaction time for drivers under