9. Hypothesis Testing for One Sample

Hospital Admissions For the matched pairs listed in Exercise 1, identify the following components used in the Wilcoxon signed-ranks test:

d. The sum of the positive ranks and the sum of the absolute values of the negative ranks

Hospital Admissions For the matched pairs listed in Exercise 1, identify the following components used in the Wilcoxon signed-ranks test:

f. The critical value of T (assuming a 0.05 significance level in a test of no difference between hospital admissions of Friday 6th and the following Friday 13th).

Correlation and Slope What is the relationship between the linear correlation coefficient r and the slope b1 of a regression line?

Appendix B Data Sets

In Exercises 13–16, use the data in Appendix B to test for rank correlation with a 0.05 significance level.

Taxis Refer to Data Set 32 “Taxis” in Appendix B and use the distances (miles) and tip amounts (dollars) of all of the rides. Is there sufficient evidence to support the claim that there is a correlation between the distance of the ride and the tip amount? Does it appear that riders base their tips on the distance of the ride?

In Exercises 1–4, use the following sequence of political party affiliations of recent presidents of the United States, where R represents Republican and D represents Democrat.

Runs Test If we use a 0.05 significance level to test for randomness, what are the critical values from Table A-10? Based on those values and the number of runs from Exercise 2, what should be concluded about randomness?

In Exercises 1–4, use the following sequence of political party affiliations of recent presidents of the United States, where R represents Republican and D represents Democrat.

Good Sample? Given the sequence of data, if we fail to reject randomness, does it follow that the sampling method is suitable for statistical methods? Explain.

In Exercises 9–12, refer to the sample data from the given exercises in Section 13-2. Use the Wilcoxon signed-ranks test for the claim about the median of a population.

 Exercise 15 “Cotinine in Smokers”

In Exercises 5–8, use the runs test with a significance level of α = 0.05. (All data are listed in order by row.)

Odd and Even Digits in Pi A New York Times article about the calculation of decimal places of π noted that “mathematicians are pretty sure that the digits of π are indistinguishable from any random sequence.” Given below are the first 25 decimal places of π. Test for randomness in the way that odd (O) and even (E) digits occur in the sequence. Based on the result, does the statement from the New York Times appear to be accurate?

In Exercises 9–12, use the runs test with a significance level of . (All data are listed in order by row.)

Testing for Randomness of Super Bowl Victories Listed below are the conference designations of teams that won the Super Bowl, where N denotes a team from the NFC and A denotes a team from the AFC. Do the results suggest that either conference is superior?

In Exercises 9–12, use the runs test with a significance level of . (All data are listed in order by row.)

Baseball World Series Victories Test the claim that the sequence of World Series wins by American League and National League teams is random. Given are recent results, with A = American League and N = National League.

Correcting the H Test Statistic for Ties In using the Kruskal-Wallis test, there is a correction factor that should be applied whenever there are many ties: Divide H

First combine all of the sample data into one list, and then, in that combined list, identify the different groups of sample values that are tied. For each individual group of tied observations, identify the number of sample values that are tied and designate that number as t; then calculate T = t3 - t . Next, add the T values to get summation_T. The value of N is the total number of observations in all samples combined.

Listed below are performance (non-verbal) IQ scores from samples of subjects with low blood lead level, medium blood lead level, and high blood lead level (from Data Set 11 “IQ and Lead” in Appendix B). For the test of equal medians, find the value of the test statistic H using the methods of this section, and then find the corrected value of H using the above correction factor. Does the corrected value of H differ substantially from the uncorrected value?

In Exercises 5–8, use (a) randomization and (b) bootstrapping for the indicated exercise from Section 9-1. Compare the results to those obtained in the original exercise.

Exercise 7 in Section 9-1 “Buttered Toast Drop”

In Exercises 5–8, use (a) randomization and (b) bootstrapping for the indicated exercise from Section 9-1. Compare the results to those obtained in the original exercise.

Exercise 8 in Section 9-1 “Tennis Challenges”

In Exercises 5–8, use (a) randomization and (b) bootstrapping for the indicated exercise from Section 9-1. Compare the results to those obtained in the original exercise.

Exercise 9 in Section 9-1 “Cell Phones and Handedness”