2. Cholesterol levels in the United States are normally distributed. In a sample

Question

2. Cholesterol levels in the United States are normally distributed. In a sample of n 15 Republicans, the cholesterol levels had a mean of 176.5 and a standard deviation of sx19.2. In a sample of m18 Democrats, the cholesterol levels had a mean ofij-- 177.1 and a standard deviation ofs, 18.9. Find a 93% confidence interval for the difference in mean cholesterol levels between Republicans and Democrats in the United States. (Assume that ?'-?, but don't use the Welch-Satterthwaite formula for degrees of freedom.) (2 points) 3. A number of minor automobile accidents occur at various high-risk intersections in Iron County. The traffic department claims that a modification in the type of light will re- duce these accidents. The county commissioners have agreed to a proposed experiment. Eight intersections were chosen at random, and the lights at those intersections were modified. The number of minor accidents during a six-month period before and after installing traffic signals were: Number of Minor Accidents ntersection efore 57 4 8 9 810 77 0 4 6 8 6 ter Find a 94% confidence interval for the difference in the number of traffic accidents. (2 points) 4. IQ scores are normally-distributed. Suppose that in a population, a sample of size n- 24 is taken. It is found that the IQ scores have a variance ofs 25.3. Construct a 96% confidence interval for the population standard deviation ? of IQ scores. (2 points)

Explanation / Answer

#2.

x1(bar) = 176.50

x2(bar) = 177.10

s1 = 19.20

s2 = 18.90

n1 = 15

n2 = 18

SE = sqrt[ (s12/n1) + (s22/n2) ]

(s12/n1) = 24.5760

(s22/n2) = 19.8450

SE = 6.6649

df = 15 + 18 - 2 = 31

x1bar - x2bar = -0.60

SE = 6.6649

CI = 93%

DF = 30

t-value = 1.8767

ME = t*SE = 12.5080

Confidence Interval is given by (x1bar - x2bar) +/- ME

Lower bound = -13.10804

Upper bound = 11.90804

Confidence Interval is (-13.108 , 11.908 )

#3.

Before After dbar 5 3 2 7 7 0 6 7 -1 4 0 4 8 4 4 9 6 3 8 8 0 10 6 4 Mean 2

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