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- Imagine that a professor of psychology has two teaching assistants (TAs) who will help her grade assignments for the duration of the semester. The professor wants to make sure that she and the TAs are well calibrated with one another, so she has all three of them grade the first assignment independently. Because the professor grades every assignment on a curve, she first converts the students’ scores to z-scores for each grader. The following table shows the z-scores for a population of 10 students in her class for each grader. Professor Teaching Assistant #1 Teaching Assistant #2 Student 1 0.70 1.27 1.27 Student 2 0.83 -0.64 -1.55 Student 3 -0.98 0.38 -0.14 Student 4 2.21 0.80 0.92 Student 5 -0.54 -1.34 -1.06 Student 6 0.43 0.10 0.30 Student 7 -1.03 -2.09 -1.50 Student 8 -0.01 0.85 1.14 Student 9 -0.54 0.48 0.57 Student 10 -1.07 0.20 0.04 The professor is going to use the z-scores to calculate the correlation coefficient between her scores…As the population ages, there is increasing concern about accident-related injuries to the elderly. An article reported on an experiment in which the maximum lean angle—the farthest a subject is able to lean and still recover in one step—was determined for both a sample of younger females (21–29 years) and a sample of older females (67–81 years). The following observations are consistent with summary data given in the article: YF: 28, 34, 32, 27, 28, 32, 31, 35, 32, 28 OF: 19, 14, 21, 13, 12 Does the data suggest that true average maximum lean angle for older females (OF) is more than 10 degrees smaller than it is for younger females (YF)? State and test the relevant hypotheses at significance level 0.10. (Use ?1 for younger females and ?2 for older females.) H0: ?1 − ?2 = 10Ha: ?1 − ?2 > 10H0: ?1 − ?2 = 10Ha: ?1 − ?2 < 10 H0: ?1 − ?2 = 0Ha: ?1 − ?2 > 0H0: ?1 − ?2 = 0Ha: ?1 − ?2 < 0 Calculate the test statistic and determine the P-value. (Round your test…As the population ages, there is increasing concern about accident-related injuries to the elderly. An article reported on an experiment in which the maximum lean angle—the farthest a subject is able to lean and still recover in one step—was determined for both a sample of younger females (21–29 years) and a sample of older females (67–81 years). The following observations are consistent with summary data given in the article: YF: 28, 34, 32, 27, 28, 32, 31, 35, 32, 28 OF: 19, 14, 21, 13, 12 Calculate the test statistic and determine the P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.) t = P-value =
- A simple linear regression model was created to examine the relationship between the age of patients (i.e. the independent variable) and the patients' scores on a questionnaire that measures quality of life (i.e. the dependent variable). There were n=20 patients in the study, and some of the results of the regression are presented below: Estimated intercept = 42 Standard error of the intercept = 13.6 Estimated slope = -0.64 Standard error of the slope = 0.52 Based on these results, which of the following can we conclude, based on an alpha level of 0.05 for significance? Question 16 options: The intercept is not significantly different from 0, but the slope is significantly different than 0. Thus, we have mixed results and we cannot make a definitive statement about the significance of the association. There is a significant association, because the intercept is statistically significantly different than 0 (p<0.05). There is not a…magine that a professor of sociology has two teaching assistants (TAs) who will help him grade assignments for the duration of the semester. The professor wants to make sure that he and the TAs are well calibrated with one another, so he has all three of them grade the first assignment independently. Because the professor grades every assignment on a curve, he first converts the students’ scores to z-scores for each grader. The following table shows the z-scores for a population of 10 students in his class for each grader. Professor Teaching Assistant #1 Teaching Assistant #2 Student 1 1.43 1.05 0.39 Student 2 -0.57 -1.33 0.87 Student 3 0.35 0.27 -0.94 Student 4 0.72 0.90 2.24 Student 5 -1.41 -1.23 -0.50 Student 6 0.10 0.27 0.56 Student 7 -2.04 -1.71 -0.94 Student 8 0.76 1.19 0.03 Student 9 0.47 0.56 -0.50 Student 10 0.18 0.03 -1.21 The professor is going to use the z-scores to calculate the correlation coefficient between his scores and…A researcher was interested in estimating the relationship between SAT scores and first year GPA. He looked at the data from a university which requires minimum SAT scores of 600 to enter the university (Note. The possible SAT score is between 200-800). The data from this experiment are presented below. Student ID SAT(X) GPA (Y) 1 680 2.4 2 745 2.1 3 670 2.2 4 720 2.5 5 653 2.0 6 710 1.8 7 675 1.8 8 634 2.3 9 690 2.4 10 711 2.3 Mean 688.8 2.18 Variance 1109 0.06 = (X −X)(Y−Y) 3.15 Compute the Pearson correlation (r) and interpret the coefficient in terms of the direction (positive or negative) and strength of the relationship (weak, moderate, or strong) Many previous studies have found that there is a strong positive relationship between SAT score and the first year GPA. Is your conclusion from question (a)…
- A researcher was interested in estimating the relationship between SAT scores and first year GPA. He looked at the data from a university which requires minimum SAT scores of 600 to enter the university (Note. The possible SAT score is between 200-800). The data from this experiment are presented below. Student ID SAT(X) GPA (Y) 1 680 2.4 2 745 2.1 3 670 2.2 4 720 2.5 5 653 2.0 6 710 1.8 7 675 1.8 8 634 2.3 9 690 2.4 10 711 2.3 Mean 688.8 2.18 Variance 1109 0.06 = 3.15 Compute the Pearson correlation (r) and interpret the coefficient in terms of the direction (positive or negative) and strength of the relationship (weak, moderate, or strong)Given are five observations collected in a regression study on two variables. xi 2 6 9 13 20 yi 7 19 7 27 21 (a) Develop a scatter diagram for these data. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 0 to 25 and is labeled: x. The vertical axis ranges from 0 to 30 and is labeled: y. The points are plotted from left to right starting in the upper left corner of the diagram. Moving from left to right, the first 3 points appear to be plotted in an upward diagonal, direction while the next 2 points are much lower on the diagram. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 0 to 25 and is labeled: x. The vertical axis ranges from 0 to 30 and is labeled: y. The points are plotted from left to right in a downward, diagonal direction starting in the upper left corner of the diagram. The points are between 7 to 27 on the vertical axis and are fairly spread out. A scatter diagram has 5 points plotted on…Suppose a researcher wants to see if the proportion of college educated adults is higher in New York compared to Florida. The researcher randomly samples 500 adults in New York and found that 196 had a college education, while a random sample of 600 adults in Florida found that 227 had a college education.At the 0.05 level of significance, does the data provide evidence to suggest the proportion of college educated adults is higher in New York than Florida? Step 1: Define the parameter & setup the testStep 2: State the Level of SignificanceStep 3: Find the value of the Test StatisticsStep 4: Find P-Value OR Find Critical ValueStep 5: State Conclusion and why
- 3. For page 12 of chapter 9 notes, the steps for completing a linear correlation hypothesis test are provided. On step 5, a conclusion sentence must be written. Which option below best describes how make a conclusion sentence for a linear regression test?On the second sheet is data which shows the rate of growth of a particular patch of bamboo vs daily high temperature.(a) Construct a scatterplot, including the equation of the line of best fit and value of R2.(b) What would the predicted growth rate be for a day with a temperature of 84◦?(c) Is there evidence, at α = 0.01, to support a claim that there is a linear relationship between temperature and growth rate? Please state clearly the null hypothesis, the alternative hypothesis, and what decision you make.Sir Francis Galton, in the late 1800s, was the first to introduce the statistical concepts of regression and correlation. He studied the relations of variables such as the size of parents and the size of their offspring. Data similar to that which he studied are given below, with the variable x denoting the height (in centimeters) of a human father and the variable y denoting the height at maturity in centimeters) of the father's oldest son. The data are given in tabular form and also displayed in the Figure 1 scatter plot. Also given are the products of the heights of fathers and heights of sons for each of the fifteen pairs
