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 118,
with standard deviation of 15. The college records indicate
that the mean IQ score for entering students from previous years
is 113. If we assume that the IQ scores of this year's
entering class are normally distributed, is there enough
evidence to conclude, at the 0.05 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
complete the parts below. Carry your intermediate computations to
three or more decimal places and round your answers as specified in
the table.
(a) State the null hypothesis H0 and
the alternative hypothesis H1
Ho:
H1:
(b) Determine the type of test statistic to use.
Z, t, chi-square or F? If it is t or chi-square, what is
the Degrees of freedom? If it is F, what is
the Degrees of freedom: dfn: dfd:
(c) Find the value of the test statistic. (Round to three
or more decimal places.
(d) Find the p-value. (Round to three or more
decimal places.
(e) Can we conclude, using the 0.05 level of
significance, that the mean IQ score of this year's class is
greater than that of previous years? Yes or No?