What is the mathematical reasoning behind how linear contrasts are used for a priori comparison of means after an ANOVA?
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- Males under the age of 25 must pay far higher auto insurance premiums than females in this age group. How does this fact relate to statistical discrimination? Statistical discrimination implies that discrimination can persist indefifinitely, while the taste-for-discrimination model suggests that competition might reduce discrimination in the long run. Explain the difference.Knee injury: The anterior cruciate ligament (ACL) runs diagonally in the middle of the knee. An article in a respected journal reports results for 94 people who had suffered ACL injuries. Of the 94 injuries, 55 were to the left knee and 39 were to the right knee. Can you conclude that the percent of ACL injuries to the left knee differs from 50%? Use the a= 0.01 level of significance. Here are the null and alternative hypotheses. Ho: P = 0.5 H₁:P +0.5 Part: 0 / 2 Part 1 of 2 (a) What is the P-value? Round your answer to four decimal places. The P-value is XAn MBA student wants to answer the question "How does an MBA major affect the number of job offers received?" He randomly sampled four recent graduates in each of the following three MBA majors [Finance (x1), Marketing(x2) and Management(x3)] and asked each of them to report the number of job offers. He obtains the following results. Sum of square between majors (SSB) = 62.17 Mean of square within majors (MSW) = 2.28 Mean number of job offers received from each MBA major are as follows: Finance major (x1) = 2.25 Marketing major (x2) = 3.25 Management major (x3) = 7.5 Construct the Analysis of Variance (ANOVA) table, and then find the SSW 62.17 20.52 82.69 SST 20.52 62.17 82.69 MSB 31.085 50 2.28 F calculated 15.45 12.20 13.36
- When should you use a one-way ANOVA to analyze your data? Distinguish between one–way ANOVA for independent groups and a one–way Repeated Measures ANOVA.A research study was conducted about gender differences in "sexting." The researcher believed that the proportion of girls involved in “sexting” is less than the proportion of boys involved. The data collected in the spring of 2010 among a random sample of middle and high school students in a large school district in the southern United States is summarized in Table. Is the proportion of girls sending sexts less than the proportion of boys "sexting?" Test at a 1% level of significance. Table 2: Frequency of "sexts" sent by gender Gender Males Females Sent "sexts" 183 156 Total number surveyed 2231 2169A research study was conducted about gender differences in “sexting.” The researcher believed that the proportion of girls involved in “sexting” is less than the proportion of boys involved. The data collected in the spring of 2010 among a random sample of middle and high school students in a large school district in the southern United States is summarized in Table. Is the proportion of girls sending sexts less than the proportion of boys “sexting?” Test at a 1% level of significance. Males Females Sent "sexts" 183 156 Total number surveyed 2231 2169
- If the difference in means of two data sets is not zero, does that imply that on average the two variables are significantly different?A recent poll randomly sampled 1100 unemployed and 950 employed Canadians and asked them about their romantic relationships. 27% of the unemployed and 26% of the employed people said they had major problems in relationships as a result of their employment status. Do the data provide convincing evidence to suggest a difference between the proportions of employed Canadians who have major relationship problems and the proportion of unemployed Canadians who have nmajor relationship problems? Provide a complete solution, showing all steps used in your analysis. This means to state the null and alternative hypothesis, make an assumption, calculate a test statistic, find a p-value, make a conclusion about the hypotheses. a.The U.S. Department of Transportation, National Highway Traffic Safety Administration, reported that 77% of all fatally injured automobile drivers were intoxicated. A random sample of 54 records of automobile driver fatalities in a certain county showed that 37 involved an intoxicated driver. Do these data indicate that the population proportion of driver fatalities related to alcohol is less than 77% in Kit Carson County? Use ? = 0.10. (a) What is the level of significance? (b) What is the value of the sample test statistic? (Round your answer to two decimal places.) c) Find the P-value of the test statistic. (Round your answer to four decimal places.)
- The forced vital capacity (FVC) is often used by physicians to assess a person's ability to move air in and out of their lungs. It is the maximum amount of air that can be exhaled after a deep breath. A researcher wants to perform a hypothesis test to determine whether the mean forced vital capacity for adults who are smokers is less than the mean forced vital capacity for adults who are former smokers. He will use a paired sample to determine whether forced vital capacity increases, on average, when adults stop smoking. Identify the two populations for the proposed hypothesis test.The personality characteristics of business leaders (e.g., CEOs) are related to the operations of the businesses that they lead (Oreg & Berson, 2018). Traits like openness to experience are related to positive financial outcomes and other traits are related to negative financial outcomes for their businesses. Suppose that a board of directors is interested in evaluating the personality of their leadership . Among a sample of n = 16 managers , the sample mean of the openness to experiences dimension of personality was M = 4.50 . Assuming that mu = 4.24 and sigma = 1.05 (Cobb -Clark & Schurer , 2012) , use a two-dailed hypothesis test with alpha = .05 to test the hypothesis that this company's business leaders ' openness to experience is different from the population .The personality characteristics of business leaders (e.g., CEOS) are related to the operations of the businesses that they lead (Oreg & Berson, 2018). Traits like openness to experience are related to positive financial outcomes and other traits are related to negative financial outcomes for their businesses. Suppose that a board of directors is interested in evaluating the personality of their leadership. Among a sample of n = 16 managers, the sample mean of the openness to experiences dimension of personality was M = 4.50. Assuming that u = 4.24 and o = 1.05 (Cobb-Clark & Schurer, 2012), use a two-tailed hypothesis test with a = .05 to test the hypothesis that this company's business leaders' openness to experience is different from the population. Standard Normal Distribution Mean - 0.0 Standard Deviation 1.0 .7198 .1401 .1401 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 -1.08 1.08 Step 1. Ho: ; H;: a = .05. Step 2. The critical region consists of Step 3. For these data the standard error is and…
