Question

A study was conducted to assess the effects that occur when children are exposed to cocaine before birth. Children were tested at age 4 for object assembly​ skill, which was described as​ "a task requiring​ visual-spatial skills related to mathematical​ competence." The 196 children born to cocaine users had a mean of 7.4 and a standard deviation of 2.9. The 183 children not exposed to cocaine had a mean score of 8.3 with a standard deviation of 3.1. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Let population 1 be children born to cocaine users

Identify the null and alternative hypotheses

State the conclusion for the test.

Answer 1

Given that,
mean(x)=7.4
standard deviation , s.d1=2.9
number(n1)=196
y(mean)=8.3
standard deviation, s.d2 =3.1
number(n2)=183
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =1.973
since our test is two-tailed
reject Ho, if to < -1.973 OR if to > 1.973
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =7.4-8.3/sqrt((8.41/196)+(9.61/183))
to =-2.914
| to | =2.914
critical value
the value of |t α| with min (n1-1, n2-1) i.e 182 d.f is 1.973
we got |to| = 2.91352 & | t α | = 1.973
make decision
hence value of | to | > | t α| and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -2.9135 ) = 0.004
hence value of p0.05 > 0.004,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: -2.914
critical value: -1.973 , 1.973
decision: reject Ho
p-value: 0.004
we have enough evidence to support the claim that difference between children born to cocaine users and children not exposed to cocaine