Concept explainers
Testing Claims About Proportions. In Exercises 7-22, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.
18. Denomination Effect A trial was conducted with 75 women in China given a 100-yuan bill, while another 75 women in China were given 100 yuan in the form of smaller bills (a 50-yuan bill plus two 20-yuan bills plus two 5-yuan bills). Among those given the single bill, 60 spent some or all of the money. Among those given the smaller bills, 68 spent some or all of the money (based on data from “The Denomination Effect,” by Raghubir and Srivastava, Journal of Consumer Research Vol. 36). We want to use a 0.05 significance level to test the claim that when given a single large bill, a smaller proportion of women in China spend some or all of the money when compared to the proportion of women in China given the same amount in smaller bills.
a. Test the claim using a hypothesis test.
b. Test the claim by constructing an appropriate confidence interval.
c. If the significance level is changed to 0.01, does the conclusion change?
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Elementary Statistics (Custom Package)
- Testing Claims About Proportions. In Exercises 7–22, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Smoking Cessation Programs Among 198 smokers who underwent a “sustained care” program, 51 were no longer smoking after six months. Among 199 smokers who underwent a “standard care” program, 30 were no longer smoking after six months (based on data from “Sustained Care Intervention and Postdischarge Smoking Cessation Among Hospitalized Adults,” by Rigotti et al., Journal of the American Medical Association, Vol. 312, No. 7). We want to use a 0.01 significance level to test the claim that the rate of success for smoking cessation is greater with the sustained care program. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval. c. Does the…arrow_forwardTesting Claims About Proportions. In Exercises 7–22, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Ground vs. Helicopter for Serious Injuries A study investigated rates of fatalities among patients with serious traumatic injuries. Among 61,909 patients transported by helicopter, 7813 died. Among 161,566 patients transported by ground services, 17,775 died (based on data from “Association Between Helicopter vs Ground Emergency Medical Services and Survival for Adults With Major Trauma,” by Galvagno et al., Journal of the American Medical Association , Vol. 307, No. 15). Use a 0.01 significance level to test the claim that the rate of fatalities is higher for patients transported by helicopter. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate…arrow_forwardTesting Claims About Proportions. In Exercises 7–22, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Cell Phones and Handedness A study was conducted to investigate the association between cell phone use and hemispheric brain dominance. Among 216 subjects who prefer to use their left ear for cell phones, 166 were right-handed. Among 452 subjects who prefer to use their right ear for cell phones, 436 were right-handed (based on data from “Hemispheric Dominance and Cell Phone Use,” by Seidman et al., JAMA Otolaryngology—Head & Neck Surgery, Vol. 139, No. 5). We want to use a 0.01 significance level to test the claim that the rate of right-handedness for those who prefer to use their left ear for cell phones is less than the rate of right-handedness for those who prefer to use their right ear…arrow_forward
- Testing Claims About Proportions. In Exercises 7–22, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Clinical Trials of OxyContin OxyContin (oxycodone) is a drug used to treat pain, but it is well known for its addictiveness and danger. In a clinical trial, among subjects treated with OxyContin, 52 developed nausea and 175 did not develop nausea. Among other subjects given placebos, 5 developed nausea and 40 did not develop nausea (based on data from Purdue Pharma L.P.). Use a 0.05 significance level to test for a difference between the rates of nausea for those treated with OxyContin and those given a placebo. a. Use a hypothesis test. b. Use an appropriate confidence interval. c. Does nausea appear to be an adverse reaction resulting from OxyContin?arrow_forwardTesting Claims About Proportions. In Exercises 7–22, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Dreaming in Black and White A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 306 people over the age of 55, 68 dream in black and white, and among 298 people under the age of 25, 13 dream in black and white (based on data from “Do We Dream in Color?” by Eva Murzyn, Consciousness and Cognition , Vol. 17, No. 4). We want to use a 0.01 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion of those under 25. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval. c. c. An explanation given for the…arrow_forwardTesting Claims About Proportions. In Exercises 7–22, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Lefties In a random sample of males, it was found that 23 write with their left hands and 217 do not. In a random sample of females, it was found that 65 write with their left hands and 455 do not (based on data from “The Left-Handed: Their Sinister History,” by Elaine Fowler Costas, Education Resources Information Center, Paper 399519). We want to use a 0.01 significance level to test the claim that the rate of left-handedness among males is less than that among females. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval. c. Based on the results, is the rate of left-handedness among males less than the rate of left-handedness among…arrow_forward
- Testing Hypotheses. In Exercises 13–24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim. Lead in Medicine Listed below are the lead concentrations (in μ g/g) measured in different Ayurveda medicines. Ayurveda is a traditional medical system commonly used in India. The lead concentrations listed here are from medicines manufactured in the United States (based on data from “Lead, Mercury, and Arsenic in US and Indian Manufactured Ayurvedic Medicines Sold via the Internet,” by Saper et al., Journal of the American Medical Association, Vol. 300, No. 8). Use a 0.05 significance level to test the claim that the mean lead concentration for all such medicines is…arrow_forwardTesting Hypotheses. In Exercises 13–24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim. Got a Minute? Students of the author estimated the length of one minute without reference to a watch or clock, and the times (seconds) are listed below. Use a 0.05 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one minute?arrow_forwardHow do you find and create a null hypothesis? Research question is : On average, are people enrolled in a Canadian post-secondary institution taller than the national average? Hypothesis: On average, people enrolled in a Canadian post-secondary institution are taller than the national average.arrow_forward
- Technology. In Exercises 9–12, test the given claim by using the display provided from technology. Use a 0.05 significance level. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim. Old Faithful Data Set 23 “Old Faithful” in Appendix B includes data from 250 random eruptions of the Old Faithful geyser. The National Park Service makes predictions of times to the next eruption, and the data set includes the errors (minutes) in those predictions. The accompanying Statdisk display results from using the prediction errors (minutes) to test the claim that the mean prediction error is equal to zero. Comment on the accuracy of the predictions. For Exercise 11arrow_forwardFinal Conclusions. In Exercises 25–28, use a significance level of α = 0.05 and use the given information for the following: a. State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0) b. Without using technical terms or symbols, state a final conclusion that addresses the original claim. Original claim: More than 58% of adults would erase all of their personal information online if they could. The hypothesis test results in a P-value of 0.3257.arrow_forwardIdentifying 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. Pulse Rates Claim: The mean pulse rate (in beats per minute, or bpm) of adult males is equal to 69 bpm. For the random sample of 153 adult males in Data Set 1 “Body Data” in Appendix B, the mean pulse rate is 69.6 bpm and the standard deviation is 11.3 bpm.arrow_forward
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