Statistics-STAT*2060DE F Questions for Assignment #6

QUESTION

STAT*2060DE FQuestions for Assignment #6This will be another D2L quiz. Please input your responses before the deadline. Give atleast 3 decimal places where applicable.Questions #1 – #8 refer to the following information.Marketing organizations sometimes use a pupillometer, a device that used to observechanges in pupil dilations as the eye is exposed to different visual stimuli, to help themevaluate potential consumer interest in mew products, alternative package designs, andother factors. Suppose one organization used a pupillometer to evaluate consumer reactionto different silverware patterns for a client. 10 consumers were chosen at random, and eachwas shown two silverware patterns. The pupillometer readings (in millimeters) are givenin the table below.Consumer12345678910Pattern A1.120.970.870.971.011.010.881.411.181.08Pattern B1.211.041.051.111.081.151.021.071.201.14N.B. We should NOT be using the independent samples method.For the following questions, take the differences using Pattern A Pattern B.#1. What is the point estimate of the population mean difference? [Hint: This valueshould be negative]#2. What is the standard error of the sample mean difference?#3. What is the 95% confidence interval for the population mean difference?A) (-.183, .069)B) (-.173, .059)C) (-.163, .049)D) (-.153, .039)E) (-.143, .029)Carry out a test that the population mean difference is equal to 0, against a two-sided1alternative.#4.What are the appropriate hypotheses?A) H0 : µ = 0, Ha : µ > 0B) H0 : µ = 0, Ha : µ = 0C) H0 : µ1 = µ2 , Ha : µ1 > µ2D) H0 : p1 = p2 , Ha : p1 = p2#5. What is the value of the appropriate test statistic? [Hint: This value should benegative.]#6. You cannot get an exact p-value from the t table, but you can get an appropriaterange of values. Which one of the following best represents what we can say about thep-value based on the t table?A) p-value <.001B) .025 < p-value <.05C) .05 < p-value <.10D) .10 < p-value <.20E) p-value >.20.#7. Which one of the following is the most appropriate conclusion at α = .05?A) There is significant evidence the population mean difference between the two patternsis equal to 0.B) There is significant evidence the population mean difference between the two patternsis not equal to 0.C) There is not significant evidence that the population mean difference differs from 0.D) All of the above.#8. For the above test to be valid, we need the sample differences to be a simple randomsample from population of differences. What is the other assumption that we need? Thatis, what else must be true in order for our methods to be reasonable?A) The population mean difference is known.B) The population of differences is normally distributed.C) The two populations have equal variance.D) The standard deviation of the population of differences is known.Questions 9-16 refer to the following information:Suppose a hotel undergoes a renovation, with the notion of catering more toward maleclientele. One year after the renovations have been completed, the hotel conducts a surveyof 24 male and 18 female guests. One question on the survey asks the customers for anoverall satisfaction rating, between 0 and 100. The following table summarizes the results.2MalesFemalesMean Rating81.862.1Standard Deviation7.16.8Sample size2418It is impossible for the ratings to be perfectly normally distributed (one reason is they’relimited to the 0-100 range). The sample sizes are not very large, but they’re not uncomfortably small either. It’s always useful to plot the data out in boxplots and normal quantileplots before using our inference procedures.The boxplots show pretty clear visual evidence of a difference in means. The normalquantile plots show some deviations from linearity, especially for the women. There are alsosome indications of extreme values in the data. When considering using the t procedures,this should give us some pause. But overall it’s not terrible, so let’s go ahead and use thet procedures here. The next question is whether we should use the Welch procedure or thepooled variance version. Since the sample standard deviations are close (7.1 vs 6.8), let’sgo with the pooled variance procedure.Use the pooled variance t procedure for the following problems. Do NOT useany large sample approximation.3#9. What is the value of the pooled sample variance?#10. What is the value of the standard error of the difference between the sample means?#11. Construct a 95% confidence interval for the difference in population means(male-females). Which one of the following is the appropriate interval?A) 19.7 ± 4.34B) 19.7 ± 4.39C) 19.7 ± 4.44D) 19.7 ± 4.49E) 19.7 ± 4.54#12. Test whether the population mean ratings for men and women are equal. Althoughone could make an argument for using a one-sided alternative that the male ratings will behigher than the female ratings on average, use a two-sided alternative. What are theappropriate hypotheses?A) H0 : xM¯B) H0 : xM¯C) H0 : µMD) H0 : µME) H0 : µM= xF ,¯= xF ,¯= µF ,= µF ,= µF ,H a : xM = xF¯¯H a : x M < xF¯¯H a : µM = µFHa : µM > µFHa : µM < µF#13. What is the value of the appropriate test statistic?#14. What is the p-value of the test? We cannot get an exact p-value from the table, butwe can find an appropriate range of values. Which one of the following is the appropriaterange?A) p-value <.001B) .001 < p-value <.002C) .01 < p-value <.02D) .05 < p-value <.10E) .1< p-value#15. Is there significant evidence of a difference in population means between men andwomen at α = .01?A)Yes.B)No.#16. Which one of the following is the most appropriate conclusion for this hypothesistest?A) We can be certain that male guests tend to give higher ratings than female guests atthis hotel.B) There is very strong evidence that the population mean rating for male guests at thishotel is greater than the population mean rating for female guests.4C) There is very strong evidence that the population mean rating for male guests at thishotel is less than the population mean rating for female guests.D) There is some evidence that the sample mean rating for male guests at this hotel isgreater than the sample mean rating for female guests at this hotel.The next series of questions refer to the following information.Suppose an insurance company is investigating the use of text messsaging by drivers in aregion. As one variable in the study, they are interested in the proportion different agegroups who have texted while driving. They conduct a large survey of drivers in the region,and find that:In a random sample of 600 drivers aged 16-19, 372 admitted to texting while driving.In a random sample of 1500 drivers aged 20-29, 745 admitted to texting while driving.#17. Calculate a 95% confidence interval for the difference in population proportions(teenage – twenties). Which one of the following is the appropriate interval?A) 0.1233 ± 0.046B) 0.1233 ± 0.048C) 0.1233 ± 0.050D) 0.1233 ± 0.052E) 0.1233 ± 0.054Test the null hypothesis that the population proportions of drivers who admit to textingwhile driving are equal for the two groups. Use a two-sided alternative.**Please call the 16-19 group Group 1. Your test statistic should be positive**#18. What are the appropriate hypotheses?A) H0 : pteen = ptwenties ,B) H0 : pteen = ptwenties ,ˆˆC) H0 : pteen = ptwenties ,D) H0 : pteen = ptwenties ,ˆˆHa : pteen > ptwentiesHa : pteen > ptwentiesˆˆHa : pteen = ptwentiesHa : pteen = ptwentiesˆˆ#19. What is the value of the test statistic?#20. The p-value of the test is closest to which one of the following?A) .01B) .05C) .10D) .20E) .50#21. Which one of the following is the most appropriate conclusion for α = .05?A) There is significant evidence that the population proportion for the 16-19 age group is5less than that of the 20-29 age group.B) There is not significant evidence of a difference between the population proportions forthe two age groups.C) There is significant evidence that the population proportions for the two age groups areequal.D) We can be certain that the sample proportions for the two age groups are equal.E) There is significant evidence that the population proportion for the 16-19 age group isgreater than that of the 20-29 age group.#22. Suppose we run a hypothesis test and obtain a p-value of .03. Which one of thefollowing statements is true?A) The null hypothesis would be rejected at α = .10, but not at α = .05.B) The null hypothesis would be rejected at α = .05, but not at α = .01.C) The null hypothesis would be rejected at α = .01.D) The null hypothesis would not be rejected at any value of α.Consider the following output for a two-sample inference procedure for the difference between population means. The output for both the pooled-variance procedure and Welch’sprocedure are given.Welch Two Sample t-testdata: temp1 and temp2t = -0.3746, df = 52.842, p-value = 0.7094alternative hypothesis: true difference in means is not equal to 095 percent confidence interval:-3.699859 2.535360sample estimates:mean of x mean of y19.54801 20.13026Pooled Variance Two Sample t-testdata: temp1 and temp2t = -0.3206, df = 53, p-value = 0.7498alternative hypothesis: true difference in means is not equal to 095 percent confidence interval:-4.224599 3.060100sample estimates:mean of x mean of y19.54801 20.13026#23. What is the p-value of the test that requires the assumption that the populationvariances are equal?#24. Which of these procedures assumes that we are sampling from normally distributedpopulations?A) Just the pooled-variance t procedure.B) Just the Welch procedure.6C) Both procedures.D) Neither procedure.#25. Which would be the more appropriate procedure in this case?A) The pooled variance procedure.B) Welch’s procedure.C) Impossible to determine with the given information.#26. Suppose we had 40 pairs of observations of A and B measurements, that resulted inthe following outputPaired t-testt = -0.3476, df = 39, p-value = 0.73alternative hypothesis: true difference in means is not equal to 095 percent confidence interval:-0.001649301 0.001165598sample estimates:mean of the differences-0.0002418514The differences were taken to be: A readings – B readings.At α = .05, which one of the following is the most appropriate conclusion?A) There is significant evidence that the readings are equal on average.B) There is significant evidence that the A readings are greater than the B readings onaverage.C) There is significant evidence that the A readings are less than the B readings on average.D) There is not significant evidence of a difference in the readings.E) We can be certain that on average there is a difference in the A and B readings.#27. The hydrostatic measurements are less time consuming, and therefore preferable ifthey provide reasonable readings when compared to the more accurate but time-intensivehydrometer readings. The winery will use the hydrostatic measurements if it can be demonstrated that the mean difference between the density measurements of the two measurements does not exceed .002. Looking at the appropriate values in the output, is therestrong evidence that the mean difference in density measurements exceeds .002?Is there strong evidence that the mean difference in measurements exceeds .002?A) Yes, there is strong evidence that the mean difference exceeds .002.B) No, there is not strong evidence that the mean difference exceeds .002.7

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