Thanks to an initiative to recruit top students, an administrator at a college claims that this year's entering class must have a greater mean IQ score than that of entering classes from previous years. The administrator tests a random sample of 13 of this year's entering students and finds that their mean IQ score is 115, with a standard deviation of 10. The college records indicate that the mean IQ score for entering students from previous years is 112.
Is there enough evidence to conclude, at the 0.10 level of significance, that the population mean IQ score, µ, of this year's class is greater than that of previous years? To answer, assume that the IQ scores of this year's entering class are approximately normally distributed.
Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)
(a) State the null hypothesis $H_0$ and the alternative hypothesis $H_1$
$H_0: \mu = 112$
$H_1: \mu > 112$
(b) Determine the type of test statistic to use.
Degrees of freedom:
(c) Find the value of the test statistic. (Round to three or more decimal places.)
0.075
(d) Find the $p$-value. (Round to three or more decimal places.)
(e) Can we conclude that the mean IQ score of this year's class is greater than that of previous years?
Yes No
