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Multiple Choice Statistics Problems

3. A chemical engineer is investigating the effect of process operating temperature on product yield. The study results in the following data; use your knowledge of least squares regression to construct a linear model for predicting yield from temperature. These data apply throughout question 3.

Temp(Celsius) Yield (grams)
100 43.6215
110 46.6231
120 58.2752
130 58.8906
140 65.4354
150 74.5960
160 72.5202
170 79.0639
180 83.6280
190 84.4351

Calculate the slope and intercept of the least squares regression model by hand, which requires only the means and standard deviations of X and Y, and the correlation coefficient (here r = 0.9805).

3 a) If the yield were measured in ounces instead of grams (note that 1 gram is 0.35274 ounces), the slope would increase by a factor of:

Answer
a. 0.35274
b. 1/0.35274
c. would not change

3 b) If the yield were measured in ounces instead of grams (note that 1 gram is 0.35274 ounces), the correlation coefficient would increase by a factor of:

Answer
a. 0.35274
b. 1/0.35274
c. would not change

4. (Look at the file attachment for the table)
Results of a two year study of the effects of calcium supplementation on bone loss are summarized below. The rate of bone loss, computed for each subject, was expressed as a percentage of their initial bone mass. Subjects were randomly allocated to three treatment groups. Group 1 received estrogen creme and a calcium placebo - Estrogen Group. Group 2 received placebo estrogen creme and 200 mg/day calcium - Calcium Group. Group 3 received placebo estrogen creme and a calcium placebo - Placebo Group.

Use one-way ANOVA to compare mean bone mass change per year for the three treatment groups and perform an F test to see if the treatment group means differ. Proceed in a step-by-step fashion doing the computations by hand (with a calculator), and answer throughout question 4.

4 a) What is the value of the grand mean computed from the above data?

Answer
a. 1.50 - 2.00
b. 2.01 - 2.25
c. 2.26 - 2.50
d. 2.51 - 2.75
e. 2.76 - 3.00

4 b) What is the value of the error sum of squares (SSE) for the above data?
(Pick the interval containing the best answer.)

Answer
a. 150 - 160
b. 161 - 170
c. 171 - 180
d. 181 - 190
e. 191 - 200

4 c) Assuming a significance level of 0.05, what is the critical value of F (F crit) for this test?

Answer
a. 3.0 - 3.5
b. 4.0 - 4.5
c. 5.0 - 5.5
d. 6.0 - 6.5
e. 7.0 - 7.5

4 d) What is the value of the F statistic for this sample of data (Fdata)?

Answer
a. 3.50 - 4.00
b. 4.01 - 4.50
c. 4.51 - 5.00
d. 5.01 - 5.50
e. 5.51 - 6.00

4 e) Is the strength of evidence against the H0 provided by the data strong enough to reject it in favor of the alternative hypothesis?

Answer
a. yes, reject H0
b. no, do not reject H0
c. can't tell.

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3.
A chemical engineer is investigating the effect of process operating temperature on product yield. The study results in the following data; use your knowledge of least squares regression to construct a linear model for predicting yield from temperature. These data apply throughout question 3.

Temp(Celsius) Yield (grams)
100 43.6215
110 46.6231
120 58.2752
130 58.8906
140 65.4354
150 74.5960
160 72.5202
170 79.0639
180 83.6280
190 84.4351

Calculate the slope and intercept of the least squares regression model by hand, which requires only the means and standard deviations of X and Y, and the correlation coefficient (here r = 0.9805).
Mean of x(temp)=(100+110+...+190)/10=145
Sxx=(100-145)^2+(110-145)^2+...+(190-145)^2=8250
Mean of yield ...

Solution Summary

The solution assists with answering the multiple choice statistics problems with a brief explanation.

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