Question

Listed in the data table are IQ scores for a random sample of subjects with medium lead levels in their blood. Also listed are statistics from a study done of IQ scores for a random sample of subjects with high lead levels. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Complete parts​ (a) and​ (b) below. Use a 0.10 significance level for both parts.

Medium lead level

72
84
92
85
83
97
83
92
97
111
91

High lead level
n2= 11

x2= 88.202

s2= 9.977

Answer 1

Solution :

Null Hyp: The mean IQ scores for medium lead level is same as high lead level

Alt Hyp: The mean IQ scores for medium lead level is greater than high lead level

Sample statistics

Medium lead level: sample mean x1 = 89.727 ; sample stdev s1 = 10.149; sample size n1 = 11

After : sample mean x2 = 88.202 ; sample stdev s2 = 9.977 ; sample size n2 = 11

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

                    = sqrt[(10.1492/11) + (9.9772/11)] = 4.291

Test stat t = [ (x1 - x2) ] / SE = [ (89.727 - 88.202) ] / 4.291 = 0.36

Degrees of Freedom DF = n1 +n2 - 2 = 20

p value for t = 0.36 and df = 20 is 0.361

Since p value > 0.10 we fail to reject the Null Hyp and conclude that there is not enough evidence to support the claim that subjects with medium lead levels have higher IQ scores

Ans) C

b) Critical value for df=20 and 0.10 sig level = +1.725

Std error = 4.291

Margin of error = critical value * std error = 1.725 * 4.236 = 7.402

Confidence interval = (x1 - x2) + Margin of error = (89.727 - 88.202) + 7.402 = (-5.877 , 8.927 )

Yes because the interval contains 0

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