BackRESAMPLING
c. When testing a claim about a proportion or mean or standard deviation, what is an important advantage of using a resampling method instead of the parametric method described in the preceding sections of this chapter?
At Least As Extreme A random sample of 860 births in New York State included 426 boys, and that sample is to be used for a test of the common belief that the proportion of male births in the population is equal to 0.512.
a. In testing the common belief that the proportion of male babies is equal to 0.512, identify the values of p^ and p.
In Exercises 13–16, write a statement that interprets the P-value and includes a conclusion about linear correlation.
Using the data from Exercise 6 “Airport Data Speeds,” the P-value is 0.003.
Simulating Dice When two dice are rolled, the total is between 2 and 12 inclusive. A student simulates the rolling of two dice by randomly generating numbers between 2 and 12. Does this simulation behave in a way that is similar to actual dice? Why or why not?
Estimates vs. Hypothesis Tests Labels on cans of Dr. Pepper soda indicate that they contain 12 oz of the drink. We could collect samples of those cans and accurately measure the actual contents, then we could use methods of Section 7-2 for making an estimate of the mean amount of Dr. Pepper in cans, or we could use those measured amounts to test the claim that the cans contain a mean of 12 oz. What is the difference between estimating the mean and testing a hypothesis about the mean?
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?
Identifying H0 and H1
In Exercises 5–8, do the following:
a. Express the original claim in symbolic form.
b. Identify the null and alternative hypotheses.
Landline Phones Claim: Fewer than 10% of homes have only a landline telephone and no wireless phone. Sample data: A survey by the National Center for Health Statistics showed that among 16,113 homes, 5.8% had landline phones without wireless phones.
Can Dogs Detect Malaria? A study was conducted to determine whether dogs could detect malaria from socks worn by malaria patients and socks worn by patients without malaria. Among 175 socks worn by malaria patients, the dogs made correct identifications 123 times. Among 145 socks worn by patients without malaria, the dogs made correct identifications 131 times (based on data presented at an annual meeting of the American Society of Tropical Medicine, by principal investigator Steve Lindsay). Use a 0.05 significance level to test the claim of no difference between the two rates of correct responses.
c. What do the results suggest about the use of dogs to detect malaria?
Independent Samples Which of the following involve independent samples?
a. Data Set 4 “Measured and Reported” includes measured heights matched with the heights that were reported when the subjects were asked for those values.
Independent Samples Which of the following involve independent samples?
b. Data Set 6 “Births” includes birth weights of a sample of baby boys and a sample of baby girls.
Independent Samples Which of the following involve independent samples?
c. Data Set 1 “Body Data” includes a sample of pulse rates of 147 women and a sample of pulse rates of 153 men.
Statistical Literacy and Critical Thinking
In Exercises 1–4, use the results from a Hankook Tire Gauge Index survey of a simple random sample of 1020 adults. Among the 1020 respondents, 86% rated themselves as above average drivers. We want to test the claim that more than 3/4 of adults rate themselves as above average drivers.
Number and Proportions
a. Identify the actual number of respondents who rated themselves as above average drivers.
At Least As Extreme A random sample of 860 births in New York State included 426 boys, and that sample is to be used for a test of the common belief that the proportion of male births in the population is equal to 0.512.
b. For random samples of size 860, what sample proportions of male births are at least as extreme as the sample proportion of 426/860?
Discarded Plastic Data Set 42 “Garbage Weight” includes weights (pounds) of discarded plastic from 62 different households. Those 62 weights have a mean of 1.911 pounds and a standard deviation of 1.065 pounds. We want to use a 0.05 level of significance to test the claim that this sample is from a population with a mean less than 2.000 pounds. Identify the null hypothesis and alternative hypothesis.
Discarded Plastic Find the test statistic used for the hypothesis test described in Exercise 1.