Exam 24: Significance, Importance, and Undetected Differences

Suppose 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.

Suppose 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.

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?

Suppose a researcher examined a relationship between taking aspirin every day (yes/no) and the incidence of a heart attack (yes/no).The sample data showed that those taking aspirin had a lower chance of incidence of heart attack.A chi-square test on the data collected resulted in a p-value less than 0.0001.The data were collected in a well-designed randomized experiment.Which of the following conclusions is appropriate?

Imagine you wish to test 4 independent hypotheses so that the total type 1 error probability is 0.10.According to the Bonferroni method, each test should be conducted at what significance level?

What is the danger of researchers only reporting on the tests that came out significant (versus reporting on all the tests they conducted)?

Large samples make it easier to detect real relationships or differences in the population than small samples (assuming everything else is equal).Explain how this is taken into account in the formula for the test statistic for testing a population mean.

Suppose 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?

Explain 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.

What 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.)

Which of the following statements is false?

Is it possible for the same relative risk to produce two different conclusions in two different statistical studies? Explain why or why not.(Assume data quality is not an issue.)

Why is it important, when reading the results of a hypothesis test, to determine whether the test was one or two sided?

The word 'significant' is often used to try to convince you that there is an important effect or relationship.Explain how this word can take on different meanings and how you need to be aware of that when consuming statistical information.

When it comes to sample size, "results may be larger (more significant) than they appear" is a good way to describe one of the possible problems with a hypothesis test.Explain how this can happen.

Suppose a group of people is interested in promoting the upcoming school tax levy.They took a survey asking people's opinion on the upcoming school tax levy (yes, no, no opinion) and they created a confidence interval for the proportion of people who were opposed to it.Their confidence interval fell completely under 50%, so less than a majority of the people oppose the levy, according to these results.Is it fair for them to conclude that "a majority of the people are in favor of upcoming school tax levy?" If yes, explain why.If no, rewrite the conclusion to be correct.

Explain why it is important to not only be aware of the proportion of people who were in favor or opposed to something, but the proportion of undecideds as well.

If 100 independent hypothesis tests are conducted using a significance level of 0.10, and if all of the null hypotheses are true, what is the expected number of false positives (type I errors)?

Explain the difference between the statistical meaning of the word 'significant results' and the regular conversational meaning of the word 'significant results.'

Is there such a thing as a sample size that was too large, in terms of producing misleading conclusions about the population? __________ (choose: yes, no)