Question

IQ scores among the general population have a mean of

100

and a standard deviation of

15

. A researcher claims that the standard deviation,

σ

, of IQ scores for males is less than

15

. A random sample of

16

IQ scores for males had a mean of

98

and a standard deviation of

10

. Assuming that IQ scores for males are approximately normally distributed, is there significant evidence (at the

0.1

level of significance) to conclude that the researcher's claim is correct?

Perform a one-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table.

The null hypothesis:	H0:
The alternative hypothesis:	H1:
The type of test statistic:	(Choose one)ZtChi squareF
The value of the test statistic: (Round to at least three decimal places.)
The critical value at the 0.1 level of significance: (Round to at least three decimal places.)
Can we support the claim that the standard deviation of IQ scores for males is less than 15 ?		Yes	No

Answer 1

The statistical software output for this problem is:

On the basis of above output:

Ho: = 15

Ha: < 15

Type of test statistic; (Chi - Square); Degrees of freedom = 15

Test statistic = 6.667

Critical value = 8.547

Can we support? Yes