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 15 of this year's entering students and finds that their mean IQ score is 113, with standard deviation of 15. The college records indicate that the mean IQ score for entering students from previous years is 112. 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 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:

The alternative hypothesis:

The type of test statistic:

The value of the test statistic (3 decimal places):

The p-value (3 decimal places):

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? |

Answer #1

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...

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