statistics

BA 376 Take -Home Midterm Name_________________________ Summer 2017 Good Luck! Some potentially useful equations: 1. A hypothesis test returns a p -value of 0.04 against the null hypothesis: First graders in 2016 were evenly split between favoring puppies, kittens, and unicorns. What is a correct interpretation of this p -value? a. Only 4% of first graders were not evenly split between these categories. b. If the first graders were evenly split between these categories, there is only a 4% chance of getting such an extreme result. c. Only 4% of first graders were evenly split between these categories. d. If the first graders really were not evenly split between these categories, there is only a 4% chance of getting such an extreme result. e. None of these is a correc t interpretation of the p -value. 2. For the same set of first graders, a researcher would like to know whether there is a difference in the proportion that prefer puppies versus the proportion th at prefer kittens. Which test statistic would be most appropria te to use in this hypothesis test? 3. For the same set of first graders, a researc her was wanting to check whether the students ’ likelihood of eating glue (yes, they have tried it/no, it’s not food) depended on which animal they favored. Which test statistic would be most appropriate to use in this hypothesis test? 4. A researcher would like to know if first graders were evenly split be tween favoring puppies, kittens , or unicorns. Which test statistic would be most appropriate to use in this hypothesis test? 5. A researcher was interested in comparing reading speeds (in words per minute) between first graders that pre fer kittens versus first graders that prefer unicorns. Because this is a new area of research, we do not have a value for either population standard deviation. Which test statistic would be most appropriate to use in this hypothesis test? 6. A researcher was interested in comparing heights between first graders that prefer puppies to first graders that prefer kittens. The researcher is willing to assum e that the population standard deviation for each of these populations is known. Which test statistic would be most appropriate to use in this hypothesis test? 7. Would it be appropriate to use the equation = ̅−0 √ ⁄ to test the difference in #6 abov e? a) Yes because this is matched (paired) data. b) Yes because this is not matched data. c) No because this is matched (paired) data. d) No because this is not matched data. e) None of the above. 8. Facebook recently estimated that 5.1% to 11.2% of its accounts were fake. Assuming this is a 95% confidence interval, what does it say about a test of the nul l hypothesis: 5% of Facebook Accounts are fake tested at 95% confidence? a) Reject the null hypothesis for this data at the given level of significance b) Fail to reject the nul l hypothesis for this data at the given level of significance c) This problem c annot be answered because the two levels of confidence are identical d) This problem cannot be answered because there is no relationship between confidence intervals and hypothesis tests. Use the following for questions 9 through 11: A study by the Robert Morris polling institute found that 44% of former football players (at any level) supported banning tackle football prior to middle school while 46% of parents supported such a ban. For the questions that follow, assume this survey was based on two independent samples , one of 350 former players and one of 650 parents of players. 9. What is the appropriate null and alternative hypothesis to check whether there was a statistically signifi cant difference between these two percentages? a) 0: ≤ , : > b) 0: < , : ≥ c) 0: = , : ≠ d) 0: ≥ , : < 10. What is the appropriate test statistic to use f or the above test? 11. What is the result of the test of the null hypothesis ( = 0.05 ) that former football players and parents of football players are equally likely to support this ban?