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.A warehouse manager wants to determine if there are productivity differences among his three shifts (morning shift, evening shift, or night shift). He measures the average number of units shipped per shift over the course of a month. He uses an ANOVA to analyze the difference among the shifts. He determined that the F value observed indicated a non-significant difference. What can he conclude from this? Data show that there is a significance difference among the 3 shifts Data show that the morning shift ships more units than the afternoon shift which ships more than the night shift Data does not indicate which shifts are different unless a Tukey's HSD test is also conducted. Data shows that the shifts have equivalent productivityA Midwest college admissions committee recently conducted a study to determine the relative debt incurred by students receiving their degrees in four years versus those taking more than four years. Some on the committee speculated a four-year student would likely be attending full time, whereas one taking more than four years could have a part-time job. However, average total debt provides only part of the information. Since the average, or mean, is affected by both large and small values, the committee also needed some way to determine the relative variances for the two groups. Samples of size 20 produced standard deviations of 2,636 for four-year graduates and 1,513 for those taking more than four years. Conduct a test of hypothesis to determine if the standard deviation of the debt for four-year graduates is larger than those taking more than four years. Use a significance level of 0.05.
- Linear contrasts for comparison of means are based on the idea of weighted averages, but how exactly does this work? Why does multiplying group means by small numbers and summing them result in a test statistic that can give more information than just comparing the means outright?A new approach for teaching mathematics was introduced that engages students in group investigations and mathematical modeling. After field tests in 36 high schools over a three-year period, researchers compared the performances the new approach students with those taught using a traditional curriculum. During the study, students in both classes that used the new approach and traditional classes took a Algebra test that did not allow them to use calculators. The accompanying table shows the results. Are the mean scores of the two groups significantly different? Write appropriate hypotheses. Let μN be the mean Algebra test score for students in classes that use the new approach. Let μT be the mean Algebra test score for students in traditional classes. b) Do you think the assumptions for inferences are satisfied? Explain. A. No. The students within each class are not independent individuals as their score on the Algebra test is dependent upon other students in the…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 2169
- 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. Males Females Sent "sexts" 183 156 Total number surveyed 2231 2169A 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.Explain the Different threats to the Internal Validity of a Multiple Regression Study?
- Let's now perform a mean-matched pairs test to test the claim that there is no mean difference between the age of males and females. For the context of this problem, d=x2−x1d=x2-x1 where the first data set represents actress (female) ages and the second data set represents male (actor) ages. We'll continue to use a significance of 0.1. You believe the population of difference scores is normally distributed, but you do not know the standard deviation. H0: μd=0H0: μd=0 H1:μd≠0H1:μd≠0 Actress Age Actor Age 34 36 27 47 35 68 31 47 36 57 37 33 27 44 36 49 22 63 33 46 31 42 26 34 25 52 What is the critical value for this test? _________ (Round to three decimal places.) What is the test statistic for this sample? _________(Round to three decimal places.) What is the p-value?________ (Round to three decimal places.) Conclusion about the null: Conclusion about the claim:Levi-Strauss Co manufactures clothing. The quality control department measures weekly values of different suppliers for the percentage difference of waste between the layout on the computer and the actual waste when the clothing is made (called run-up). The data is in the table, and there are some negative values because sometimes the supplier is able to layout the pattern better than the computer. Do the data show that there is a difference between some of the suppliers? Test at the 1% level. Run-ups for Different Plants Making Levi Strauss Clothing Plant Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 3 Plant 3 Plant 3 Plant 3 Plant 3 Plant 3 Plant 3 Plant 3 Plant 3 Plant 3 Plant…Levi-Strauss Co manufactures clothing. The quality control department measures weekly values of different suppliers for the percentage difference of waste between the layout on the computer and the actual waste when the clothing is made (called run-up). The data is in the table, and there are some negative values because sometimes the supplier is able to layout the pattern better than the computer. Do the data show that there is a difference between some of the suppliers? Test at the 1% level. Run-ups for Different Plants Making Levi Strauss Clothing Plant Difference Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 1 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 2 Plant 3 Plant 3 Plant 3 Plant 3 Plant 3 Plant 3 Plant 3 Plant 3 Plant 3…
