9. Hypothesis Testing for One Sample

Interpreting P-value The Ericsson method is one of several methods claimed to increase the likelihood of a baby girl. In a clinical trial, results could be analyzed with a formal hypothesis test with the alternative hypothesis of p > 0.5 which corresponds to the claim that the method increases the likelihood of having a girl, so that the proportion of girls is greater than 0.5. If you have an interest in establishing the success of the method, which of the following P-values would you prefer as a result in your hypothesis test: 0.999, 0.5, 0.95, 0.05, 0.01, 0.001? Why?

Can a critical value for the chi-square test be negative? Explain.

Performing a Sign Test In Exercises 7–22, (a) identify the claim and state Ho and Ha, (b) find the critical value, (c) find the test statistic, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.

Hourly Wages A labor organization claims that the median hourly wage of podiatrists is at least \$70.00. In a random sample of 23 podiatrists, 17 earn less than \$70.00 per hour, 5 earn more than \$70.00 per hour, and 1 earns \$70.00 per hour. At , can you reject the labor organization’s claim? (Adapted from U.S. Bureau of Labor Statistics)

Reading Rates (See Problem 22 in Section 10.3.) Michael Sullivan, son of the author, decided to enroll in a reading course that allegedly increases reading speed and comprehension. Prior to enrolling in the course, Michael read 198 words per minute (wpm). The following data represent the words per minute read for 10 different passages after the course.

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a. The goal of the research is to determine if the words read per minute has increased as a result of the reading course. Based on this research objective, state the null and alternative hypotheses.

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?

Writing Hypotheses: Internet Provider An Internet provider is trying to gain advertising deals and claims that the mean time a customer spends online per day is greater than 28 minutes. You are asked to test this claim. How would you write the null and alternative hypotheses when

a. you represent the Internet provider and want to support the claim?

HIC Measurements Listed below are head injury criterion (HIC) measurements from crash tests of small, midsize, large, and SUV vehicles. In using the Kruskal-Wallis test, we must rank all of the data combined, and then we must find the sum of the ranks for each sample. Find the sum of the ranks for each of the four samples.

Performing a Runs Test In Exercises 15 – 20, (a) identify the claim and state H0 and Ha, (b) find the critical values, (c) find the test statistic, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Use α = 0.05

[APPLET] Dog Identifications A team of veterinarians record, in order, the genders of every dog that is microchipped at their pet hospital in one month. The genders of recently microchipped dogs are shown, where F represents a female and M represents a male. A veterinarian claims that the microchips are random by gender. Do you have enough evidence to reject the doctor’s claim?

M M F M F F F F F M M M F F

F M F F F F F M F F F M F F F

Interpreting a Decision In Exercises 43–48, determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that

a. rejects the null hypothesis?

A recent study claims that at least 20% of renters are behind on rent payments in New Jersey. 

Explain how to use the sign test to test a population median.

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?

Requirements Assume that we want to use the data from Exercise 1 with the Kruskal-Wallis test. Are the requirements satisfied? Explain.

Which of the following correctly describes the steps for testing a hypothesis using the $p$-value approach, including verifying the requirements of the test?

Which of the following is the initial step in conducting a hypothesis test?

Which of the following is not a requirement for testing means in hypothesis testing?