a statistician wishing to test a hypothesis that students score 75% on the final

Question

a statistician wishing to test a hypothesis that students score 75% on the final exam in an introductory statistics course to randomly select 20 students in the class and have them take the exam early. The average score of the 20 students on the exam was 72% and the standard deviation in the population is known to be sigma=15%.The statitician calculates the test statitics to be -0.8944. If the statitician chose to do a two-sided alternative, teh pvalue would be calculated by finding the are to the:

right of the absolute value of -.8944 and dividing it by two
left of -.8944 and doubling it
left of-.8944
left of -.8944 and doubling it

Explanation / Answer

Let me explain this via example

In our example concerning the mean grade point average, suppose again that our random sample of n = 15 students majoring in mathematics yields a test statistic t* instead equaling -2.5. The P-value for conducting the two-tailed test H0 : = 3 versus HA : 3 is the probability that we would observe a test statistic less than -2.5 or greater than 2.5 if the population mean really were 3. That is, the two-tailed test requires taking into account the possibility that the test statistic could fall into either tail (and hence the name "two-tailed" test). The P-value is therefore the area under a tn - 1 = t14 curve to the left of -2.5 and to the right of the 2.5. It can be shown using statistical software that the P-value is 0.0127 + 0.0127, or 0.0254:

So answer is left of -.8944 and doubling it

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