Suppose that the mean on an I.Q. test is known to be 100 for the general populat

Question

Suppose that the mean on an I.Q. test is known to be 100 for the general population. We are interested in whether a particular group of children in a kindergarten class score significantly higher or lower than the typical mean I.Q. score. We obtain a sample of the 20 children, administer the I.Q. test to them, and get the following results:
M=103 and =10.

a.                  What are the null and alternative hypotheses for this situation?
b.                  What is the estimated standard error of the mean?
c.                  Perform the appropriate statistical test, with =.05.
d.                  Describe the results of your findings. Is this test statistically significant? Why or why not?
e.                  Compute the 95% confidence interval.
f.                    Compute the effect size.

Explanation / Answer

Question a)

Null Hypothesis (Ho): µ = 100

Alternative Hypothesis (Ha): µ ¹ 100

Question b)

SE = sigma / sqrt (n) = 10/sqrt(20) = 2.2361

The estimated standard error of the mean is 2.2361

Question c)

z = ( x bar – Mean ) / SE

= (103-100)/ 2.2361

= 1.34

Question d)

The critical z at 5% level of significance from normal table we get as (-/+) 1.96.

Here 1.34 falls in between the critical values (-1.96 and 1.96). We fail to reject the null hypothesis.

There is not sufficient evidence to conclude that a kindergarten class score significantly higher or lower than the typical mean I.Q. score.

Question e)

Confidence Interval:

X bar (-/+) E

X bar = 103

E = zc * ( sigma / sqrt (n)) = 1.96 * (10/sqrt(20)) = 4.38

X bar (-/+) E

103 (-/+ ) 4.38

98.62 and 107.38

The 95% confidence interval is (98.62 and 107.38)

Question e)

Effect size = (103-100)/10 = 0.3

The value of the effect size is 0.3

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