BackFinding Critical Values
In Exercises 17–20, refer to the information in the given exercise and use a 0.05 significance level for the following.
a. Find the critical value(s).
b. Should we reject H0 or should we fail to reject H0?
Exercise 14
Finding Critical Values
In Exercises 17–20, refer to the information in the given exercise and use a 0.05 significance level for the following.
a. Find the critical value(s).
b. Should we reject H0 or should we fail to reject H0?
Exercise 15
Finding Critical Values
In Exercises 17–20, refer to the information in the given exercise and use a 0.05 significance level for the following.
a. Find the critical value(s).
b. Should we reject H0 or should we fail to reject H0?
Exercise 16
Minting Dollar Coins For the sample data from Exercise 1, we get a P-value of 0.0041 when testing the claim that σ < 0.04000 g.
What should we conclude about the null hypothesis?
What should we conclude about the original claim?
What do these results suggest about the new minting process?
Finding Critical Values of (chi)^2 For large numbers of degrees of freedom, we can approximate critical values of as follows:
(chi)^2 = (1/2)(z + sqrt(2k-1))
Here k is the number of degrees of freedom and z is the critical value(s) found from technology or Table A-2. In Exercise 12 “Spoken Words” we have df = 55, so Table A-4 does not list an exact critical value. If we want to approximate a critical value of (chi)^2 in the right-tailed hypothesis test with α = 0.01 and a sample size of 56, we let k =55 with z = 2.33 (or the more accurate value of z = 2.326348 found from technology). Use this approximation to estimate the critical value of for Exercise 12. How close is it to the critical value of (chi)^2 = 82.292 obtained by using Statdisk and Minitab?
RESAMPLING
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?
Hypothesis Testing. In Exercises 17–19, apply the central limit theorem to test the given claim. (Hint: See Example 3.)
Adult Sleep Times (hours) of sleep for randomly selected adult subjects included in the National Health and Nutrition Examination Study are listed below. Here are the statistics for this sample: n = 12, x_bar = 6.8 hours, s = 20 hours. The times appear to be from a normally distributed population. A common recommendation is that adults should sleep between 7 hours and 9 hours each night. Assuming that the mean sleep time is 7 hours, find the probability of getting a sample of 12 adults with a mean of 6.8 hours or less. What does the result suggest about a claim that “the mean sleep time is less than 7 hours”?
4 8 4 4 8 6 9 7 7 10 7 8
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.
In Exercises 5–20, assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with “Table” answers based on Table A-3 with df equal to the smaller of n1-1 and n2-1)
Better Tips by Giving Candy An experiment was conducted to determine whether giving candy to dining parties resulted in greater tips. The mean tip percentages and standard deviations are given below along with the sample sizes (based on data from “Sweetening the Till: The Use of Candy to Increase Restaurant Tipping,” by Strohmetz et al., Journal of Applied Social Psychology, Vol. 32, No. 2).
a. Use a 0.05 significance level to test the claim that giving candy does result in greater tips.
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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?