1:43 PM Southern Virginia University Aaron Steele MacFarlane 3) Your fascination

Question

1:43 PM Southern Virginia University Aaron Steele MacFarlane 3) Your fascination with teenagers has led you to do several things. First, in your research, you discover that the average IQ of 8th graders is 100, with a standard deviation of 15. You want to see how 8th graders in BV compare to 8th graders in your home town, so you collect 2 SRS: 200 8th graders from BV 400 8th graders from your hometown (not BV) Suppose the means were 96.2 for the BV sample and 100.9 for your hometown sample. Calculate and interpret 90% confidence intervals. Would your interpretation change if you calculated 99% confidence intervals instead? Font Family Font Sizes B | Y A. .

Explanation / Answer

Sol:

For BV sample

n=sample size=200

sample mean=96.2

sd=15

z crit for 90%=1.645

90% confidence interval for population mean is

samplemean-zcrit(samplesd/sqrt(n),samplemean+zcrit(samplesd/sqrt(n)

96.2-1.645(15/sqrt(200),96.2+1.645(15/sqrt(200)

94.46,97.94

lower limit=94.46

upper limit=97.94

94.46<population mean<97.94

Intrrepretation:

we are 90% confident that the true population mean lies in between

94.46 and 97.94

For hometown sample:

90% confidence interval for population mean is

samplemean-zcrit(samplesd/sqrt(n),samplemean+zcrit(samplesd/sqrt(n)

100.9-1.645(15/sqrt(400),100.9+1.645(15/sqrt(400)

99.67,102.13

lower limit=99.67

upper limit=102.13

we are 90% confident that the true popualtion mean lies in between 99.67 and 102.13

For 99% put z crit=2.576

For BV sample:

99% confidence interval for population mean is

samplemean-zcrit(samplesd/sqrt(n),samplemean+zcrit(samplesd/sqrt(n)

96.2-2.576(15/sqrt(200),96.2+2.576(15/sqrt(200)

93.47,98.93

lower limit=93.47

upper limit=98.93

For Hometowm sample:

99% confidence interval for population mean is

samplemean-zcrit(samplesd/sqrt(n),samplemean+zcrit(samplesd/sqrt(n)

100.9-2.576(15/sqrt(400),100.9+2.576(15/sqrt(400)

98.97,102.93

lower limti=98.97

upper limit=102.93

We are 99% confident that the true popuklation mean of hometown sample lies in between

98.97 and 102.93

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