21. Which of the following would substantially reduce the size of the confidence interval?S1:‘Enlarge both the random samples of first and third year students to 1,000.’S2:‘Increase the number of bootstrap samples to 1,000,000.’S3:‘Increase the confidence level to 99.9999%.’S4:‘Use a powerful supercomputer to obtain the bootstrap distribution.’A) S1 only.B) S1 and S2 only.C) S1, S2 and S3 only.D) All of them.E) None of them.

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22. Which of the following are valid conclusion(s)?S1:‘We are 95% sure that there is a substantial difference between first and thirdyear undergraduate students in terms of time spent on social networks.’S2:‘We are 95% sure thatμ1-μ3is between 2.4 and 7.6.’S3:‘We are 95% sure that ¯x1-¯x3is between 2.4 and 7.6.’S4:‘The probability thatμ1-μ3lies between 2.4 and 7.6 is 0.95.’

23. Suppose that a 95% confidence interval forμis (54.4, 60.4). Which of the following ismost likely thep-value for the test ofH0:μ=54 versusHa:μ6=54?

24. In an experiment, individual subjects are usually allocated to treatments using randomassignment. The reason for using random assignment is to

25. Increasing the significance level of a hypothesis test (say, from 5% to 10%) will cause thep-value of an observed test statistic to . . .A) increaseB) decreaseC) stay the sameD) become undeterminedE) hard to say without information on the sample size.

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26. A bootstrap distribution, based on 1,000 bootstrap samples is provided. Use the distributionto estimate a 99% confidence interval for the population mean.

27. Percentiles of a bootstrap distribution are provided. Use the percentiles to report a 95%confidence interval for the parameter.1%2.5%5%10%25%50%75%90%95%97.5%99%6.176.326.446.596.877.177.487.787.958.088.30

28. At the start of 2012 the city of Greensville implemented legal reforms that allowed morepeople to move there from Bluetown. During 2012, 100 people were murdered in Greensville,whereas the murder rate had been stable at about 50 people per year during 2000–2011.There is an election for mayor coming up and a candidate makes the following argument:the city needs to restrict further immigration from Bluetown because otherwise the murderrate will be over 500 per year by 2025. Which statistical fallacy/fallacies has the candidatemade?