Based on the IQ scores for 19 of her children, Michelle Duggar performs a hypoth

Question

Based on the IQ scores for 19 of her children, Michelle Duggar performs a hypothesis test to see if her children (M IQ score = 120) are significantly (sigma = .01) more intelligent than the average person in the population at large (mu IQ score = 100, sigma = 15). What is the z-score for her sample and the most appropriate decision and conclusion for this hypothesis test? z = 1.333; Reject the null hypothesis. Results suggest the Duggar children are significantly more intelligent than the population at large. z = 1.333; Reject the null hypothesis. Results suggest the Duggar children are not significantly more intelligent than the population at large. z = 1.333; Fail to reject the null hypothesis. Results suggest the Duggar children are significantly more intelligent than the population at large. z = 1.333; Fail to reject the null hypothesis. Results suggest the Duggar children are not significantly more intelligent than the population at large. z = 5.812; Reject the null hypothesis. Results suggest the Duggar children are significantly more intelligent than the population at large. z = 5.812; Reject the null hypothesis. Results suggest the Duggar children are not significantly more intelligent than the population at large.

Explanation / Answer

Given that,
population mean(u)=100
standard deviation, =15
sample mean, x =120
number (n)=19
null, Ho: <100
alternate, H1: >100
level of significance, = 0.01
from standard normal table,right tailed z /2 =2.326
since our test is right-tailed
reject Ho, if zo > 2.326
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 120-100/(15/sqrt(19)
zo = 5.81187
| zo | = 5.81187
critical value
the value of |z | at los 1% is 2.326
we got |zo| =5.81187 & | z | = 2.326
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : right tail - ha : ( p > 5.81187 ) = 0
hence value of p0.01 > 0, here we reject Ho
ANSWERS
---------------
null, Ho: =100
alternate, H1: >100
test statistic: 5.81187
critical value: 2.326
decision: reject Ho
p-value: 0
z = 5.812; Reiect the null hypotheSS. results suggest the Duggar children are significantly more intelligent than
the population at Large.

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