SOLUTION: a. The average IQ is 100, with a population standard deviation of 15. The mayor of Smartsville claims that citizens in his town have higher than average IQs. To test that claim, 4

Question 1161497: a. The average IQ is 100, with a population standard deviation of 15. The mayor of Smartsville claims that citizens in his town have higher than average IQs. To test that claim, 40 Smartsville citizens were randomly selected, and their average IQ was determined to be 104.1. Does this support the mayor’s claim? Use α = 0.1.

b. construct a 90 % confidence interval for the mean. Does the confidence interval support the claim made in part a?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
This is a z-test with the usual assumptions
z=(x bar-mean)/sigma/sqrt (n)
Critical value is |z|>1.645
z=(104.1-100)*sqrt(40)/15
=1.73
reject Ho and the average IQ is not 100 in Smartsville, it is higher, p-value is 0.084
90% CI half-interval is z*sigma/sqrt(40) with z=1.645
half-interval is 3.90
add and subtract from/to mean
90% Confidence interval is (100.2, 108), and because 100 is not in the interval, is consistent with rejection of Ho in a.

RELATED QUESTIONS
A principal claims that the students in his school are above average intelligence. A... (answered by Edwin McCravy)

The average IQ is 100. The distribution is normal with a standard deviation of 15. A. (answered by Boreal)

IQ test scores are standardized to produce a normal distribution with a mean of u=100... (answered by ewatrrr)

Supposed that an IQ score has a bell shape distribution with population of 100 and... (answered by Boreal)

Mensa is an organization whose members possess IQ that are in the top 2% of the... (answered by ewatrrr)

IQ scores of adults are normally distributed with a mean of 100 and a standard deviation... (answered by stanbon,ewatrrr)

4. Membership in Mensa requires an IQ score above 131.5. Seven candidates take IQ tests,... (answered by solver91311)

IQ as measured by the Wechsler Adult Intelligence Test, is scaled so that the mean in the (answered by stanbon)

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. If... (answered by stanbon,edjones)