Appendix A (Multiple Choice Questions on Statistical Significance)Self-developed multiple choice questions - Stat 217 finalQuestions 1-7 concern the following scenario:You want to investigate a claim that women are more likely than men to dream in color. You takea random sample of men and a random sample of women (in your community) and ask whether they dream in color. Note: A “statistically significant” difference provides convincing evidence (e.g., small p-value) ofa difference between men and women – This note is optional to include.1) If the difference in the proportions (who dream in color) between the two groups turns out not to be statistically significant, which of the following is the best conclusion to draw?26% a) You have found strong evidence that there is no difference between the groups.62% b) You have not found enough evidence to conclude that there is a difference between the groups.12% c) Because the result is not significant, the study does not support any conclusion.2) If the difference in the proportions (who dream in color) between the two groups does turn out to be statistically significant, which of the following is a valid conclusion? 12% a) It would not be surprising to obtain the observed sample results if there is really no difference between men and women. 82% b) It would be very surprising to obtain the observed sample results if there is really nodifference between men and women.6% c) It would be very surprising to obtain the observed sample results if there is really a difference between men and women.3) Suppose that the difference between the sample groups turns out not to be significant, even though your review of the research suggested that there really is a difference between men and women. Which conclusion is most reasonable?6% a) Something went wrong with the analysis.6% b) There must not be a difference after all.88% c) The sample size might have been too small.4) If the difference in the proportions (who dream in color) between the two groups does turn out to be statistically significant, which of the following is a possible explanation for this result?8% a) Men and women do not differ on this issue but there is a small chance that random sampling alone led to the difference we observed between the two groups.30% b) Men and women differ on this issue.62% c) Either (a) or (b) are possible explanations for this result.5) Reconsider the previous question. Now think about not possible explanations but plausible explanations. Which is the more plausible explanation for the result?28% a) Men and women do not differ on this issue but there is a small chance that random sampling alone led to the difference we observed between the two groups.36% b) Men and women differ on this issue.36% c) They are equally plausible explanations.6) Suppose that two different studies are conducted on this issue. Study A finds that 40 of 100 women sampled dream in color, compared to 20 of 100 men. Study B finds that 35 of 100 women dream in color, compared to 25 of 100 men. Which study provides stronger evidence thatthere is a difference between men and women on this issue?78% a) Study A2% b) Study B20% c) The strength of evidence would be similar for these two studies7) Suppose that two more studies are conducted on this issue. Both studies find that 30% of women sampled dream in color, compared to 20% of men. But Study C consists of 100 people ofeach sex, while Study D consists of 40 people of each gender. Which study provides stronger evidence that there is a difference between men and women on this issue?82% a) Study C 8% b) Study D10% c) The strength of evidence would be similar for these two studies8) You plan to use a random sample of students at your school to investigate a claim that the average amount spent on the most recent haircut by the population is more than $15. Why would a large (random) sample be better than a small one?a) Because you’re more likely to get extreme haircut prices with a larger sample.b) Because larger samples produce less variability in haircut prices within sample results.c) Because larger samples produce less variability in average haircut prices from sample to sample.(CAOS) 9) Researchers surveyed 1,000 randomly selected adults in the U.S. A statistically significant, strong positive relationship was found between income level and the number of containers of recycling they typically collect in a week. Please select the best interpretation of thisresult.a) We cannot conclude that earning more money causes more recycling among U.S. adults because this type of design does not allow us to infer causation.b) This sample is too small to draw any conclusions about the relationship between income level and amount of recycling for adults in the U.S.c) This result indicates that earning more money influences people to recycle more than people who earn less money.10) Alicia wants to know if she receives higher tips, on average, when she gives customers her name compared to when she does not. She decides to track her tips for one week keeping track ofthe amounts and whether she gives the customers her name or not. She finds that giving her name led to a statistically significant higher average tip amount. Of the options below, what additional information is necessary for Alicia to be able to conclude that giving her name causes ahigher tip, on average?a) The number of tables where she does and does not give her nameb) The method Alicia used to decide which tables she would tell or not tell her namec) No additional information is necessary because the result was statistically significantCAOS questions - Post-calculus students with ISCAM text19. A graduate student is designing a research study. She is hoping to show that the results of an experiment are statistically significant. What type of p-value would she wantto obtain?0% A large p-value. 100% A small p-value (vs. 67.9% national comparison group)0% The magnitude of a p-value has no impact on statistical significance. A research article reports the results of a new drug test. The drug is to be used to decreasevision loss in people with Macular Degeneration. The article gives a p-value of .04 in the analysis section. … Indicate if each interpretation is valid or invalid. 25. The probability of getting results as extreme as or more extreme than the ones in this study if the drug is actually not effective.76.2% Valid 23.8% Invalid (vs. 57.1%)26. The