In order to assess the efficacy of a training program, 5 trainees were randomly selected. Each trainee was tested twice; once before the training program and once after the training program. Based on the following test scores, Trainee Score before 1 2 3 4 5 8 7 6 8 9 training Score after training 10 8 9 -- 10 Test the hypothesis that the training program was effective (i.e., the mean score after training is greater than the mean score before training. (Use α = 0.05)
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- What is meant by the sample space of an experiment?Independent random samples of 27 people living on the west side of a city and 26 people living on the east side of a city were taken to determine if the income levels of west side residents are less than the income levels of east side residents. Given the testing statistics below, determine if the data provides sufficient evidence to conclude that the income levels of west side residents are less than the income levels of east side residents, at the 4% significance levelIs College Worth It? In the New York Times article “College Graduates Fare Well in Jobs Market, Even through Recession,” C. Rampell noted that college graduates have suffered through the recession and lackluster recovery with remarkable resilience. Of a random sample of 1020 college graduates, 35 were unemployed; and of a random sample of 1008 high-school graduates (no college), 69 were unemployed. a. At the 1% significance level, do the data provide sufficient evidence to conclude that college graduates have a lower unemployment rate than high-school graduates? b. Find and interpret a 98% confidence interval for the difference in unemployment rates of college and high-school graduates.
- 3. Hypothesis Testing: Comparing Two Population ParametersIn 1980, of 750 men 20-34 years old, 130 were found to be overweight. Whereas, in 1990, of 700 men, 20-34 years old, 160 were found to be overweight. At the 5% significance level, do the data provide sufficient evidence to conclude that, for men 20-34 years old, a higher percentage were overweight in 1990 than 10 years earlier? Conduct the test using the p-value approach.An article claimed that "those with a college degree reported a higher incidence of sunburn than those without a high school degree—45 percent versus 26 percent." For purposes of this exercise, suppose that these percentages were based on random samples of size 200 from each of the two groups of interest (college graduates and those without a high school degree). Is there convincing evidence that the proportion who experience a sunburn is higher for college graduates than it is for those without a high school degree? (Use pcollege graduates − pwithout a high school degree. Round your test statistic to two decimal places and your P-value to four decimal places.) z = P =People who were born between 1978 and 1983 are sometimes classified by demographers as "Generation Y". According to a Forrester Research survey published in American Demographics (Vol. 22(1), p. 12), of 850 Generation Y Web users, 459 reported using the Internet to download music. At the 5% significance level, does the data provide sufficient evidence to conclude that a majority of Generation Y Web users use the Internet to download music? Use the One-Proportion z-test and interpret your result.
- A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that certification level is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 27 physicians from each of the three certification levels—Board certified (C); Uncertified, board eligible (E); and Uncertified, board ineligible (I)—and recorded the total per-member, per-month charges for each (a total of 27 physicians). In order to compare the mean charges for the three groups, the data will be subjected to an analysis of variance. Write the null hypothesis tested by the ANOVA.A management dean claims that out of 14,700 students who took the midterm examination, 10,016 received a leakage of the test. To validate this claim, a random sample of 800 has been selected, and 506 of them had received an examination leakage. At 1% significance level, is there sufficient evidence to reject the dean’s claim? a. Use the critical-value approach.b. Use the ?-value method.For a statistics class project, a college student randomly samples 75 men who exercise at a gym regularly and 68 women who exercise at a gym regularly. The college student records the number of minutes each person exercises in a given week. The college student believes that the mean number of minutes per week is lower for men than for women. The college student conducts a hypothesis test at the 5% significance level. What conclusion can you draw from the output? The data provide sufficient evidence to reject the null hypothesis and to conclude that the mean number of minutes exercised per week is lower for men than for women. The data provide sufficient evidence to conclude that there is no difference in the mean number of minutes exercised per week for men and women. The data do not provide sufficient evidence to conclude that the mean number of minutes exercised per week is lower for men than for women. We accept the null hypothesis, and conclude that there is a difference in…
- An economist is studying salaries for high technology companies and wants to test the claim that the average salary for high tech employees is less than $70,000. The economist selects a sample of 35 random employees from various high tech companies and records their salaries. Based on past studies, the economist determines that the population standard deviation is $8,500. The economist conducts a one-mean hypothesis test at the 5% significance level to test the claim that the average salary for high tech employees is less than $70,000. Which is the correct setup for the null and alternative hypothesis for this example? Select the correct answer below: H0:μ=70,000; Ha:μ<70,000, which is a left-tailed test. H0:μ=70,000; Ha:μ>70,000, which is a right-tailed test H0:μ<70,000; Ha:μ=70,000, which is a left-tailed test. H0:μ>70,000; Ha:μ=70,000, which is a left-tailed test.An agency that hires out clerical workers claims its workers can type, on average, at least 60 words per minute (wpmwpm). To test the claim, a random sample of 50 workers from the agency were given a typing test, and the average typing speed was 58.8 wpmwpm. A one-sample tt-test was conducted to investigate whether there is evidence that the mean typing speed of workers from the agency is less than 60 wpmwpm. The resulting pp-value was 0.267. Which of the following is a correct interpretation of the pp-value? The probability is 0.267 that the mean typing speed is 60 wpmwpm or more for workers from the agency. A The probability is 0.267 that the mean typing speed is 60 wpmwpm or less for workers from the agency. B The probability is 0.267 that the mean typing speed is 58.8 wpmwpm or less for workers from the agency. C If the mean typing speed of workers from the agency is 60 wpmwpm, the probability of selecting a sample of 50 workers with mean 58.8…