Question

2 7 2 020 My Notes O Ask Your The folowing data represent crime rates per 1000 population for a rendom sample of 46 Denver neighborhoods. 63.2 36.3 26.2 53.2 65.3 32.0 6s.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 73.8 715 58.5 67.2 78.6 33.2 4.9 45.1 132.1 104.7 63.2 59.6 75.7 9.2 69.9 87.5 560 154.2 85.5 77.5 4.7 24.2 37.5 41.1 (a) use α cakulator with mean and sample standard deviation keys to find the sample mean x and ampte standard denoton s' (Round your answers te on, some, Pace) crimes per 1000 people crimes per 1000 people (b) Let us say te preceding data are representative of the population enne rates·n Denver neighborhoods. Compute an 806 confidence intervalfura, the population mean enme rate for as Denve neighborhoods. (Round your answers to one decimal plece) lower Smit upper limit crimes per 1000 people crimes per 1000 people (c) Suppose you are advising the police departrent about potre patrol ด.vgnments. On-seighbortood he.. orne rite of so omes per 1000 ponoton. О。you thnk that this rate " below the average population cnme rate and that fewer patrals could selely be asigned to this neihrhood? Use the covdence interva to stity your anewer Yes. The confidence interval indicates that this cme rate is belew the average population eme rate Yes. The confidence interval indicates that this cme rale does not dffer from the average pepulation e O No. The confidence interval indicates that this crme rate is belaw the average popuiaton erime rate O No. The confidence interval indicates that this crme rate does not differ from the average popuiation cime race has a crime rate of 75 nimes per 1030 population. Does this crime rate seem to be higher than the population average? Would you recommend essigning more patrols t (a) Another "จ%erhood this neighborhoos? Use the confidence iterval to justily your answer ves. The confidence intervei indcates that this crme rate does not dimer from the average populacion crime rate. Yes. The conidence interval indicates that this crme rate is higher than the everage populetien ereme ate. O No. The confidence interval indicates that this onme rate is higher than the average population crime rate. O No. The confidence interval indicates that this crime rate does not differ from the average population ome rate. arsen, to ene denal Pin) populatien meen crime rate for an Dene iegtoorhoods. CRovd (e) Computo . 95% confidence interval fr", the ower tmit erimes per 1000 people

Answer 1

(a)

Mean $\bar{x}$ = 64.2

Standard deviation, s = 27.9

(b)

Standard error of sampling distribution of mean = s/ $\sqrt{n}$ = 27.9 / $\sqrt{46}$ = 4.113631

Degree of freedom, df = n-1 = 46 - 1 = 45

Critical value of t for 80% confidence interval and 45 degree of freedom = 1.3

Lower limit = 64.2 - 4.113631 * 1.3 = 58.9

Upper limit = 64.2 + 4.113631 * 1.3 = 69.5

(c)

As, the value 59 lies in the 80% confidence interval, the answer is,

No, The confidence interval indicates that this crime rate does not differ from the average population crime rate.

(d)

As, the value 75 is above the upper limit of 80% confidence interval, the answer is,

Yes, the confidence interval indicates that this crime rate is higher than the average population crime rate.

(e)

Critical value of t for 95% confidence interval and 45 degree of freedom = 1.3

Lower limit = 64.2 - 4.113631 * 2.014 = 55.9

Upper limit = 64.2 + 4.113631 * 2.014 = 72.5

(f)

As, the value 59 lies in the 95% confidence interval, the answer is,

No, The confidence interval indicates that this crime rate does not differ from the average population crime rate.

(g)

As, the value 75 is above the upper limit of 80% confidence interval, the answer is,

Yes, the confidence interval indicates that this crime rate is higher than the average population crime rate.

(h)

No, According to the central limit theorem, when n $\ge$ 30, the $\bar{x}$ is approximately normal.