A researcher theorizes that first-born children of African-American families are

Question

A researcher theorizes that first-born children of African-American families are more intelligent than other African-American children. A sample of 50 first-born children of African-American families is found to have an average IQ of 105, while based on other studies we can assume that IQ of other African-American children is 100 on average and has standard deviation of 15. What is the population of interest in this study?

A. All African-American families

B. All African-American children

C. IQ of African-American children

D. IQ of all first-born African-American children

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Explanation / Answer

Given that,
population mean(u)=105
sample mean, x =100
standard deviation, s =15
number (n)=50
null, Ho: =105
alternate, H1: <105
level of significance, = 0.05
from standard normal table,left tailed t /2 =1.677
since our test is left-tailed
reject Ho, if to < -1.677
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =100-105/(15/sqrt(50))
to =-2.357
| to | =2.357
critical value
the value of |t | with n-1 = 49 d.f is 1.677
we got |to| =2.357 & | t | =1.677
make decision
hence value of | to | > | t | and here we reject Ho
p-value :left tail - Ha : ( p < -2.357 ) = 0.01123
hence value of p0.05 > 0.01123,here we reject Ho
ANSWERS
---------------
null, Ho: =105
alternate, H1: <105
test statistic: -2.357
critical value: -1.677
decision: reject Ho
p-value: 0.01123
we have enough evidence to support the claim that first-born children of African-American families are more intelligent than other African-American children
option:
D
IQ of all first-born African-American children

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