Homework SourseThese 31 girls are an SRS of all seventhgrade girls in the s
| These 31 girls are an SRS of all seventh-grade girls in the school district. Suppose that the standard deviation of IQ scores in this population is known to be = 15. We expect the distribution of IQ scores to be close to Normal. Below is the distribution\'s stemplot.
True or False: There are no major departures from Normality. | ||||||||||||||
| 7. | Estimate the mean IQ score for all seventh-grade girls in the school district, using a 90% confidence interval. | ||||||||
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| These 31 girls are an SRS of all seventh-grade girls in the school district. Suppose that the standard deviation of IQ scores in this population is known to be = 15. We expect the distribution of IQ scores to be close to Normal. Below is the distribution\'s stemplot.
True or False: There are no major departures from Normality. | ||||||||||||||
Solution
A)
TRUE: There are no major departures from Normality.
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Note that
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.05
X = sample mean = 105.8387097
z(alpha/2) = critical z for the confidence interval = 1.644853627
s = sample standard deviation = 14.27140912
n = sample size = 31
Thus,
Lower bound = 101.6225867
Upper bound = 110.0548326
Thus, the confidence interval is
( 101.6225867 , 110.0548326 )
[ANSWER, the closest is OPTION B: 101.41 to 110.27.
I think your instructor used tables, and that will introduce some round off errors.]
