Suppose researchers tell you that they did not find a statistically significant relationship between two variables, and the p-value was .84 . Which of the following must be true?
a. The sample size must have been small.
b. There must not be a relationship in the population.
c. There must not have been a relationship observed in their sample.
d. None of the above.
Q. 2Suppose a pilot study tells you that there is a great deal of natural variability in the population. How will this impact the design of your actual, full blown study?
a. It will cause you to take a larger sample than you may have originally planned on.
b. It will cause you to abandon the bigger study; you won't be able to detect any differences or relationships even if they did exist.
c. Since there is so much variability, you might as well use a smaller sample size, because smaller sample sizes have more variability as well.
d. The pilot study shouldn't impact your design at all; that would be data snooping.'
Q. 3Which of the following statements is false?
a. A small enough sample size could miss even the strongest of relationships that exists in a population.
b. Small sample sizes make it harder to rule out the null hypothesis.
c. A test based on a small sample size has less statistical power than a test using a large sample size, even if the percentages, means, and other statistics found in the sample are the same in both situations.
d. None of the above.
Q. 4Suppose a researcher conducted a 2-sided hypothesis test for a population mean (significance level .05) and his test statistic was +1.84 . (The significance level was .05.) He knows this test statistic is not large enough to reject the null hypothesis, because the test statistic was not greater than 1.96 . Then he realizes that if he had done a one-sided test to begin with (alternative hypothesis > ) his results would have been statistically significant, because his test statistic was greater than 1.65 . At this point, he decides to change to a one-sided hypothesis test, and reports his results as being statistically significant. Is this acceptable? Why or why not.
Q. 5Suppose a researcher examines a possible relationship in the population and the results are found to not be statistically significant. Can the researcher conclude that there was no significant relationship in the population? If yes, explain why; if no, describe how the researcher should state their conclusion regarding a possible relationship.
Q. 6Suppose a company says they deliver their packages in 2 days or less, on average, and you are concerned that the packages are taking longer to deliver than promised. You conduct a hypothesis test to help you answer this question. Which alternative hypothesis would give you the best chance of detecting an actual problem, a one-sided alternative (average time of delivering packages is greater than 2 days) or a two-sided alternative (average time delivering packages is not equal to 2 days)? Explain your answer. If both have the same chance, explain why.
Q. 7Explain how the natural variability in the population can affect a test's ability to detect a difference or relationship in the population that actually does exist.
Q. 8What is the statistical reason that small samples result in a harder time detecting real relationships or differences in the population than large samples? (Assume data quality is not an issue.)
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