The following data represent crime rates per 1000 population fora random sample of 46 Denver neighborhoods.†
| 63.2 | 36.3 | 26.2 | 53.2 | 65.3 | 32.0 | 65.0 |
| 66.3 | 68.9 | 35.2 | 25.1 | 32.5 | 54.0 | 42.4 |
| 77.5 | 123.2 | 66.3 | 92.7 | 56.9 | 77.1 | 27.5 |
| 69.2 | 73.8 | 71.5 | 58.5 | 67.2 | 78.6 | 33.2 |
| 74.9 | 45.1 | 132.1 | 104.7 | 63.2 | 59.6 | 75.7 |
| 39.2 | 69.9 | 87.5 | 56.0 | 154.2 | 85.5 | 77.5 |
| 84.7 | 24.2 | 37.5 | 41.1 |
(a) Use a calculator with mean and sample standard deviationkeys to find the sample mean x and sample standarddeviation s. (Round your answers to one decimalplace.)
| x = | crimes per 1000 people |
| s = | crimes per 1000 people |
(b) Let us say the preceding data are representative of thepopulation crime rates in Denver neighborhoods. Compute an 80%confidence interval for ?, the population mean crime ratefor all Denver neighborhoods. (Round your answers to one decimalplace.)
| lower limit | crimes per 1000 people |
| upper limit | crimes per 1000 people |
(c) Suppose you are advising the police department about policepatrol assignments. One neighborhood has a crime rate of 62 crimesper 1000 population. Do you think that this rate is below theaverage population crime rate and that fewer patrols could safelybe assigned to this neighborhood? Use the confidence interval tojustify your answer.
Yes. The confidence interval indicates that this crime rate isbelow the average population crime rate.Yes. The confidenceinterval indicates that this crime rate does not differ from theaverage population crime rate. No. Theconfidence interval indicates that this crime rate is below theaverage population crime rate.No. The confidence interval indicatesthat this crime rate does not differ from the average populationcrime rate.
(d) Another neighborhood has a crime rate of 75 crimes per 1000population. Does this crime rate seem to be higher than thepopulation average? Would you recommend assigning more patrols tothis neighborhood? Use the confidence interval to justify youranswer.
Yes. The confidence interval indicates that this crime rate doesnot differ from the average population crime rate.Yes. Theconfidence interval indicates that this crime rate is higher thanthe average population crime rate. No. Theconfidence interval indicates that this crime rate is higher thanthe average population crime rate.No. The confidence intervalindicates that this crime rate does not differ from the averagepopulation crime rate.
(e) Compute a 95% confidence interval for ?, thepopulation mean crime rate for all Denver neighborhoods. (Roundyour answers to one decimal place.)
| lower limit | crimes per 1000 people |
| upper limit | crimes per 1000 people |
(f) Suppose you are advising the police department about policepatrol assignments. One neighborhood has a crime rate of 62 crimesper 1000 population. Do you think that this rate is below theaverage population crime rate and that fewer patrols could safelybe assigned to this neighborhood? Use the confidence interval tojustify your answer.
Yes. The confidence interval indicates that this crime rate isbelow the average population crime rate.Yes. The confidenceinterval indicates that this crime rate does not differ from theaverage population crime rate. No. Theconfidence interval indicates that this crime rate is below theaverage population crime rate.No. The confidence interval indicatesthat this crime rate does not differ from the average populationcrime rate.
(g) Another neighborhood has a crime rate of 75 crimes per 1000population. Does this crime rate seem to be higher than thepopulation average? Would you recommend assigning more patrols tothis neighborhood? Use the confidence interval to justify youranswer.
Yes. The confidence interval indicates that this crime rate doesnot differ from the average population crime rate.Yes. Theconfidence interval indicates that this crime rate is higher thanthe average population crime rate. No. Theconfidence interval indicates that this crime rate is higher thanthe average population crime rate.No. The confidence intervalindicates that this crime rate does not differ from the averagepopulation crime rate.
(h) In previous problems, we assumed the x distributionwas normal or approximately normal. Do we need to make such anassumption in this problem? Why or why not? Hint: Use thecentral limit theorem.
Yes. According to the central limit theorem, when n ?30, the x distribution is approximately normal.Yes.According to the central limit theorem, when n ? 30, thex distribution is approximatelynormal. No. According to the central limittheorem, when n ? 30, the x distribution isapproximately normal.No. According to the central limit theorem,when n ? 30, the x distribution is approximatelynormal.
