Bivariate data relating the number of classroom absences and the number of points earned prior to the final exam in the course was gathered from a random sampling of students. Plot a scatter diagram. Find the correlation coefficient and the simple regression line. Place this line on the scatter diagram. Is the relationship significant? A student with 7 absences would probably have how many points in the course? A student with 20 absences would probably have how many points?
Physicians feel that there is a relationship between a person's age and the number of days they are sick that year. A random sample of 20 was obtained to this end comparing age and days sick. Plot a scatterdiagram. Find the correlation coefficient and give alpha levels for significance. Find the regression line and place it on the scatter diagram. How many days in a year would you predict that a 60 year old person will be sick?
Two different teaching methods are being compared to the traditional (lecture) method of teaching calculus. Method one (computer) uses the computer for homework, exploratory projects, drill on concepts, and testing (by random computer generated tests). Method two (project) uses a graphing calculator, weekly projects to guide students through concepts, class discussion, and student presentations. Random samples of student exam scores from each of the three groups (lecture, computer, and project) are to be compared. Assume the following:
According to final exam scores seen in the three samples, which approach, if any does the best job of teaching calculus? Construct an ANOVA table, state the null hypothesis, give the test statistic clearly, give your conclusion and interpret. Remember to follow your ANOVA with appropriate tests if there is a significant difference.
An experiment was conducted to compare the wearing qualities of three types of paint. Ten point specimens were tested for each paint type and the number of hours until visible abraision was apparent was recorded. Assume that the variances are not significantly different, that the distributions are approximately normal, that the measures are numerical. Is there evidence to indicate a difference in the three plant types? Give all appropriate information. Each group has 10 readings with the following statistics: $$\begin{array}{l|c|c} & s & \bar{x}\\\hline \textrm{Type 1} & 158.196 & 229.6\\\hline \textrm{Type 2} & 147.874 & 309.9\\\hline \textrm{Type 3} & 196.818 & 427.8\\\hline \end{array}$$ $$SS_{\textrm{between}} = 198772 \quad SS_{\textrm{within}} = 770671$$
It is believed that there is a relationship between intelligence as measured by IQ scores on the Otis Lennin Test (OLT), with a population mean of 100 and a standard deviation of 15, and the achievement as measured by the PSAT, with a population mean of 95 and a standard deviation of 15. Bivariate data relating OLT and PSAT scores was obtained from a random sample of 10th graders taking the PSAT test at a local high school.
You have been asked to determine if one brand of fertilizer is better than another. Seedlings are obtained. Each grouping of seedlings has the same conditions except for the type fertilizer used. Growth (in inches) for fertilizer A, fertilizer B, and fertilizerC are recorded after 2 months. Answer using the following statistical model:
For a random sample of 12 people, their initial weights and weight lost from a diet for one month (both in pounds) are recorded. (a) Draw a scatter diagram. Give the equation for the regression line and draw the regression line on the scatter diagram. (b) Is there a significant linear correlation between the two variables? Give the critical value for the test. (c) What is the best predicted weight loss for an individual with an initial weight of 165 pounds?