BackA human resources department is comparing two employee training programs to see if they lead to different pass rates on a required certification exam. They randomly select two groups of employees. In Program A, 16 out of 20 employees passed the exam. In Program B, 30 out of 40 employees passed. Are the basic conditions met to conduct a 2-proportion hypothesis test?
A school administrator wants to compare the proportion of students who passed a standardized math exam in two different schools by taking samples from 2 classes. Assume the samples are random and independent. Calculate the -score for testing whether there is a significant difference in the population proportions of student passing rates, but do not find a -value or draw a conclusion for the hypothesis test.
Class A: 72 out of 120 students passed.
Class B: 65 out of 100 students passed.
A researcher using a survey constructs a 90% confidence interval for a difference in two proportions. According to the data, they calculate with a margin of error of 0.07. Should they reject or fail to reject the claim that there is no difference in these two proportions?
The data below is taken from two random, independent samples. Calculate the margin of error for a 99% confidence interval for the difference in population proportions.
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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.
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.
c. If the significance level is changed to 0.01, does the conclusion change?
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.
c. Does nausea appear to be an adverse reaction resulting from OxyContin?
Color and Creativity Researchers from the University of British Columbia conducted trials to investigate the effects of color on creativity. Subjects with a red background were asked to think of creative uses for a brick; other subjects with a blue background were given the same task. Responses were scored by a panel of judges and results from scores of creativity are given below. Use a 0.05 significance level to test the claim that creative task scores have the same variation with a red background and a blue background.
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Color and Recall Researchers from the University of British Columbia conducted trials to investigate the effects of color on the accuracy of recall. Subjects were given tasks consisting of words displayed on a computer screen with background colors of red and blue. The subjects studied 36 words for 2 minutes, and then they were asked to recall as many of the words as they could after waiting 20 minutes. Results from scores on the word recall test are given below. Use a 0.05 significance level to test the claim that variation of scores is the same with the red background and blue background.
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Testing Effects of Alcohol Researchers conducted an experiment to test the effects of alcohol. Errors were recorded in a test of visual and motor skills for a treatment group of 22 people who drank ethanol and another group of 22 people given a placebo. The errors for the treatment group have a standard deviation of 2.20, and the errors for the placebo group have a standard deviation of 0.72 (based on data from “Effects of Alcohol Intoxication on Risk Taking, Strategy, and Error Rate in Visuomotor Performance,” by Streufert et al., Journal of Applied Psychology, Vol. 77, No. 4). Use a 0.05 significance level to test the claim that both groups have the same amount of variation among the errors.
Second-Hand Smoke Samples from Data Set 15 “Passive and Active Smoke” include cotinine levels measured in a group of smokers ( n = 40, x_bar = 172.48 ng/mL, 119.50 ng/mL ) and a group of nonsmokers not exposed to tobacco smoke ( n = 40, x_bar = 16.35 ng/mL, 62.53 ng/mL ). Cotinine is a metabolite of nicotine, meaning that when nicotine is absorbed by the body, cotinine is produced.
a. Use a 0.05 significance level to test the claim that the variation of cotinine in smokers is greater than the variation of cotinine in nonsmokers not exposed to tobacco smoke.
Second-Hand Smoke Samples from Data Set 15 “Passive and Active Smoke” include cotinine levels measured in a group of smokers ( n = 40, x_bar = 172.48 ng/mL, 119.50 ng/mL ) and a group of nonsmokers not exposed to tobacco smoke ( n = 40, x_bar = 16.35 ng/mL, 62.53 ng/mL ). Cotinine is a metabolite of nicotine, meaning that when nicotine is absorbed by the body, cotinine is produced.
b. The 40 cotinine measurements from the nonsmoking group consist of these values (all in ng/mL): 1, 1, 90, 244, 309, and 35 other values that are all 0. Does this sample appear to be from a normally distributed population? If not, how are the results from part (a) affected?
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.
b. Test the claim by constructing an appropriate confidence interval.
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.
Cigarette Pack Warnings A study was conducted to find the effects of cigarette pack warnings that consisted of text or pictures. Among 1078 smokers given cigarette packs with text warnings, 366 tried to quit smoking. Among 1071 smokers given cigarette packs with warning pictures, 428 tried to quit smoking. (Results are based on data from “Effect of Pictorial Cigarette Pack Warnings on Changes in Smoking Behavior,” by Brewer et al., Journal of the American Medical Association.) Use a 0.01 significance level to test the claim that the proportion of smokers who tried to quit in the text warning group is less than the proportion in the picture warning group.
a. Test the claim using a hypothesis test.