Question

A certain intelligence test has an N(100, 100) distribution. To see whether intelligence is inherited, tests are given to the eldest child of each of a random sample of 16 acclaimed scholars. The average score of the children is 105.

a. Give the null hypothesis to be tested.

b. Give the alternative hypothesis.

c. Perform the test.

d. How likely is it that data like these represent a sample from a population in which the null hypothesis is true?

Answer 1

Sol:ution-A:

Null hypothesis,Ho:

Solution-B:

Alternative hypothesis,Ho:

c. Perform the test.

pop mean=100

pop variance=100

pop standard dev=sqrt(!00)=10

z=xbar-mu/sigma/sqrt(n)

=(105-100)/(10/qrt(16)

=5/(10/4)

z=2

p==2*(1-righttail)

right tail p=

NORM.S.DIST(2,TRUE)

=0.977249868

Therefore

P=2*(1-0.9772)

P=0.0455

P<0.05

reject null hypothesis

Accept alternative hypothesis

There is no sufficient evidence at 5% level of significance that

intelligence is inherited

d. How likely is it that data like these represent a sample from a population in which the null hypothesis is true?

likely is it that data like these represent a sample from a population in which the null hypothesis is true=p value=0.0455

u= 100

001 +11