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 12 of this year's entering students and finds that their mean IQ score is 115, with a standard deviation of 9. 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 0.05 level of significance, that the population mean IQ score, u, of this year's class is greater than that of previous years? Assume that the IQ scores of this year's entering class are approximately normally distributed.

Perform a one-tailed test.

Carry your intermediate computations to 3 or more decimal places

a). State the null and alternative hypothesis

b). Determine the type of test statistic to use

c). Find the value of the test statistic ( round to 3 or more decimal places)

d). Find the p-value ( round to 3 or more decimal places)