Question

We suspect that the IQs of students at a certain college tend to run above the national average of 100. It is also known, according to past experience, that the distribution of IQ has a standard deviation of 10. a. Set up appropriate null and alternative hypotheses. b. If a random sample of size n = 35 is drawn from the student body of the college and a mean of 104 is observed, what inference can we draw at (alpha) = 0.01 ? (You are told that the t-value for a one-tailed test with 34 degrees of freedom and 1% significance is 2.44.)

Answer #1

We have given that S=10 , n=35,

(a)The null and alternative hypotheses:

This corresponds to a right-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

(b) *Rejection
Region*

Based on the information provided, the significance level is
*α*=0.01, and the critical value for a right-tailed test is
tc = 2.44.

The rejection region for this right-tailed test is R = {t: t > 2.44}

*Test
Statistics*

The t-statistic is computed as follows:

*Decision about the
null hypothesis*

Since it is observed that
, it is then concluded that *the null hypothesis is not
rejected.*

*Conclusion*

There is not enough evidence to claim that the population mean
*μ* is greater than 100, at the 0.01 significance level.

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