SHOW ALL YOUR WORK
1. Consider the following 10 data points: x 3 5 6 4 3 7 6 5 4 7 y 4 3 2 1 2 3 3 5 4 2
(a) Plot the above observations on a scatterplot.
(b) Calculate the correlation coefficient, r (by hand). What does this value tell us?
(c) Calculate the least squares regression line.
2. A foods-and-nutrition investigator would like to know if the amount of sodium (g) can be predicted by the amount of sugar (g) in the following sample of 12 popular breakfast cereals.
Cereal Sugar (g) Sodium (g)
Mini Wheats 7 0
All-Bran 5 0.26
Apple Jacks 14 0.13
Captain Crunch 12 0.22
Cheerios 1 0.29
Cinnamon Toast Crunch …show more content…
13 0.21
Corn Flakes 2 0.29
Raisin Bran 12 0.21
Oat Bran 10 0.14
Crispix 3 0.22
Frosted Flakes 11 0.20
Fruit Loops 13 0.13
(a) Identify the response and explanatory variables.
(b) Use JMP output given below and highlight the least squares regression line on the output. Interpret the slope of the least squares regression line in the context of this question.
(c) What is the percentage of variation in sodium that is explained by its regression on sugar? (d) What is the residual for Captain Crunch?
(e) Using your JMP output, what is the value of the correlation coefficient?
(f) Suppose we calculated sodium and sugar in milligrams (mg) instead of grams (g).
What effect would that have on the correlation coefficient?
(g) Is Mini Wheats an outlier or an influential observation? Explain. (no calculations required). (h) What is the predicted sodium content of a cereal with 28 grams of sugar? Is this prediction reliable? Explain.
3. You have been asked to develop an experiment to meet the objectives for each of the following scenarios. For each of the studies, answer the following questions:
i. What is the appropriate type of experimental design that should be used? ii. What are the experimental units? iii. What is/are the factor(s) under investigation? iv. What are the factor levels?
v. What are the treatments to be applied? vi. Is there a blocking variable? If so, what is it? vii. Draw a chart to outline the proposed design of the experiment.
(a) A tire manufacturer would like to determine how weather conditions and speed affect the stopping distance of a vehicle using a certain type of tire.
An experiment will be conducted on a test track under simulated weather conditions (either dry, rain or snow) and at different speeds (40 km/h, 60 km/h, 80 km/h or 100 km/h).
Each combination of factor levels will be tested in three trial runs.
(b) An experiment is to be conducted to determine the effect of temperature on the adhesive strength of C-glue. The glue will be applied to a material at either 10ºC, 15ºC or 20ºC. The experiment will be conducted separately for two different types of material (metal and plastic), as the effect of temperature is expected to differ for the two materials. Ten pieces of metal and ten pieces of plastic will be tested for each treatment.
4. A running-shoe manufacturer wanted to test the effect of its new sprinting shoe on the 100-meter dash times. The company sponsored five athletes who were running the 100- meter dash in the Summer Olympics. To test the shoe, it had all five runners run the race with its competitor's shoe and then again with its new shoe. The company used the difference in times as its response
variable.
(a) Suggest some improvements to this design.
(b) Why might the shoe manufacturer not be able to generalize the results they found to all runners?
5. In September 1998, USA Weekend magazine asked, “Should humans be cloned?" Readers were invited to register a \Yes" or \No" answer by calling one of two different 800 numbers. Based on 38023 responses, the magazine reported that “9 out of 10 readers oppose cloning." Is this conclusion justified? Why or why not? If not, describe the types of bias that may be present.
.
(a) Describe a sampling strategy to randomly select those to be searched.
(b) Here is the first-class passenger list and a set of random digits. Select two passengers to be searched, carefully demonstrate your process.
65436 71127 04879 41516 20451 02227 917469 23593
Bergman Cox Fontana Perl
Bowman DeLara Forester Rabkin
Burkin Dell Frongillo Roi
Castillo Dugan Furnas Swafford
Clancy Febo LePage Testut