Statistical Hypothesis Testing and Two-sided Test

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Practice with p-values
Work through these problems with your computer partner and/or instructor. Answers follow the problem set.
1. Suppose we’ve done the computation of the Z test statistic. For each of the following situations determine the p-value that goes along with Z.
a. Z = 2.12, two-sided test
b. Z = 4.55, two-sided test
c. Z = -1.40, lower-tail test
2. Suppose Z = 1.92.Which has a smaller p-value, the upper-tail test or the two-sided test? From this, is it more likely to have a result that is significant at the 5% level using-a one-sided test or using a two-sided test?
3. Agricultural researchers at K-State sometimes study how diets affect the weight gain of animals. Suppose a standard diet gives an average weight gain of 20 lbs., and we would like to know whether or not a new diet gives a greater average weight gain than this. We test H0: population mean = 20 versus Ha: population mean > 20.
a. In one study, we have a random sample of 30 animals. The sample mean is 22 and the standard deviation is 10. What is the one-sided p-value for the test and what is our conclusion?
b. In another study we have a random sample of 100 animals. Again the sample mean is 22 and the standard deviation is 10. What is the one-sided p-value and what is our conclusion?
c. All other things being equal, if we take a larger sample size do we get a larger or smaller p-value? answer next page

Answers
1. a. p = area above 2.12 and below -2.12. This is .0170 + .0170 = .0340. Note that the 2sided p-value is always double the one-sided p-value.
b. p is area greater than 4.55 and less than -4.55. This is zero to 4 decimals. So p < .0001.
c. p is area less than -1.40, p = .0808.
2. The upper-tail p-value is the area greater than 1.92 which is p = .0274. This is statistically significant at the 5% level of significance. The two-sided p-value is .0274 +
.0274 = .0548 which is not significant at the 5% level of significance. The two-sided pvalue for a z-test

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