Table 1: Table for Exercise 1.VICTIMS Frequency Percent--------------------------------0 1244 90.81 81 5.92 27 2.03 11 0.84 4 0.35 2 0.16 1 0.1N Mean Std Dev-----------------------1370 0.146 0.546PRACTICE QUESTIONS FOR EXAM 11. The 1990 General Social Survey asked respondents, “During the past 12 months,how many people have you known personally that were victims of homicide.”Table 1 shows a computer printout from analyzing responses for 13 70 subjects.a. Does the Empirical Rule apply to this distribution. Why or why not?b. Based on the mean and standard deviation, explain what you would surmiseabout the shape of the distribution.2. Find the z-score for the upp er quartile of a normal distribution.3. According to Current Population Reports, self-employed individuals in the UnitedStates in 19 90 worked an average of 44.6 hours per week, with a standard de-viation of 14.5. Assuming this variable is approximately normally distributed,find the proportion who averaged more than 40 hours per week.4. The 199 1 General Social Survey a sked, “During the last year, did anyone takesomething from you by using force – such as a stickup, mugging, or threat?”Of 987 subjects, 17 answered yes and 970 answered no.a. Construct a 95% confidence interval for the population proportion whowould answer yes.b. Interpret the interval in (a ) .15. A significance test is conducted about the value of a population mean, to seewhether it differs from 100. The sample of 100 observatio ns have a mean of 97and a standard deviation of 30.a. Define notation, and state the hypotheses.b. Find the test statistic.c. Find the P -value, and interpret.d. For the α-level of .05, what would be your conclusion about the null hy-pothesis?For the following multiple-choice items, select the correct response(s).6. (5 pts.) The standard error of a statistic describesa. The standard deviation of the sampling distribution of that statistic.b. The standard deviation of the sample measurements.c. How close that statistic is likely to fa ll to the parameter that it estimates.d. The variability in the values of the statistic for repeated random samplesof size n.e. The error that occurs due to nonresponse and measurement errors (such aslying to the interviewer).7. (4 pts.) The Central Limit Theorem implies thata. All variables have approximately bell-shaped sample distributions if a ran-dom sample conta ins at least 30 observations.b. Population distributions are normal whenever the population size is larg e.c. For large random samples, the sampling distribution ofy is approximatelynormal, regardless of the shape of the population distribution.d. The sampling distribution looks more like the population distribution asthe sample size increases.e. All of the above.8. (5 pts.) Based on responses of 1467 subjects in General Social Surveys in themid-1980s, a 95% confidence interval for the mean number of close friends equals(6.8, 8.0). Which of the following interpretations is (are) correct?a. We can be 95% confident thatY is between 6.8 and 8.0.b. We can be 95% confident that µ is between 6.8 and 8.0.c. Ninety-five percent of the values of Y = number of close friends (for thissample) are between 6 .8 and 8.0.2d. If random samples of size 1467 were repeatedly selected, then 95% of thetime Y would be between 6.8 and 8.0.e. If random samples of size 1467 were repeatedly selected, then in the longrun 9 5% of the confidence intervals formed would contain the true valueof µ.Indicate true (T) or false (F):9. Outliers have a greater impact on the mean than the median.10. We want to determine the sample size needed to obtain a good estimate of apopulation proportion π. To be “conservative” in determining the answer, interms of having a sample size that is safe even if somewhat larger than actuallyneeded, we can assume that π = 0 or π = 1.Solutions1. a. No, distribution not even approximately bell-shaped. b. Highly skewed tothe right.2. z = 0.673. About 0.624.a. 0.017 ± 0.008, or (0.009, 0.025). b. We can be 95% confident that the popu-lation proportion who would answer yes is between 0.009 and 0.025.5.a. H0: µ = 100, Ha: µ 6= 100. b. t = −1.0. c. P = 0.32. If H0is true, theprobability would be 0.32 of getting a sample mean at least as far from 10 0 as theobserved sample mean (or, a t statistic at least 1.0 in absolute value). d. Do notreject H0. It is plausible that µ = 100.6. a, c, d7. c8. b, e9. T10. F3Formulasy =Σyins2=Σ(y −y)2n − 1σy=σ√nz =y − µσy ± t(se), se = s/√nt =y − µ0seσˆπ=sπ(1 − π)nˆπ ± z(se), se =sˆπ(1 − ˆπ)nz =ˆπ − π0se0se0=sπ0(1 − π0)nn =zM2π(1 − π)n