Question

A college professor claims that the entering class this year appears to be smarter than entering classes from previous years. He tests a random sample of

10

of this year's entering students and finds that their mean IQ score is

121

, with standard deviation of

14

. The college records indicate that the mean IQ score for entering students from previous years is

111

. If we assume that the IQ scores of this year's entering class are normally distributed, is there enough evidence to conclude, at the

0.1

level of significance, that the mean IQ score,

μ

, of this year's class is greater than that of previous years?

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. (If necessary, consult a list of formulas.)

The null hypothesis:	H0:
The alternative hypothesis:	H1:
The type of test statistic:	(Choose one)ZtChi squareF	Degrees of freedom:
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 conclude, using the 0.1 level of significance, that the mean IQ score of this year's class is greater than that of previous years?		Yes	No

Answer 1

This is the right tailed test .

The null and alternative hypothesis is

H₀ : = 111

H_a : > 111

Test statistic = t

= ( - ) / s / n

= (121 - 111) / 14 / 10

= 2.259

Test statistic = 2.259

degrees of freedom = 9

= 0.1

Critical value = 1.383

Reject the null hypothesis .

Yes