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STAT 512

FINAL EXAM

Instructions: This is a take-home exam. You are not allowed to consult with anyone regarding the exam.

Multiple Choice: Each multiple choice question is worth 3 points.

1. For a fixed sample size, if the level of significance is changed from 0.01 to 0.05 with all else remaining constant, then the probability of Type II error for the test will

A) not be changed

B) become smaller

C) become larger

D) become larger or smaller depending on other factors

2. A hypothesis test for equality of four population means was conducted. The value of the p-value was less than the specified level of significance, 0.05. If the population means were all equal, then the decision from this test

A) was a Type I error

B) was a Type II error

C) was correct

D) was none of the above

3. For a survey of 900 college students, the following table gives mean classes missed per week classified by gender and whether or not students are in a Greek organization (sorority/fraternity).

| |Greek organization member? |

|Gender |No |Yes |

|Female |1.23 |1.24 |

|Male |1.67 |2.13 |

Based on the means given in the table, it appears that gender and Greek organization membership (no or yes) are

A) not interacting variables because members of Greek organization miss more classes per week than non-members do, regardless of gender.

B) interacting variables because the difference between non-members and members of Greek organizations is greater for males than it is for females.

C) interacting variables because males miss more classes than females.

D) not interacting variables because males miss more classes than females regardless of Greek membership.

4. In a two-factor ANOVA problem, there are 4 levels of factor A, 5 levels of factor B, and 2 observations (replications) for each combination of levels of the two factors. Then, the number of treatments in this experiment is

A) 40

B) 11

C) 10

D) 20

5. In the fixed effects model with interaction, assume that there are 3 levels of factor A, 2 levels of factor B, and 3 observations for each of the six combinations of levels of the two factors. Then the critical value for testing the null hypothesis of no interaction between the levels of the two factors at the .05 significance level is

A) 3.89

B) 3.00

C) 3.49

D) 3.55

6. On a survey conducted at a university, students were asked how they felt about their weight (about right, overweight, or underweight), and also were asked to record their grade point average (GPA). There were 234 responses, with 160 saying their weight was about right, 50 said they were overweight, and 17 underweight. The question of interest is whether mean GPA is the same or differs for different weight attitude populations. Minitab output for the study is given below.

|Source DF SS MS F P |

|Wt_Feel 2 2.134 1.067 4.98 0.008 |

|Error 232 49.719 0.214 |

|Total 234 51.852 |

|Individual 95% CIs For Mean |

|Based on Pooled StDev |

|Level N Mean StDev -----+---------+---------+---------+- |

|about_ri 160 3.0952 0.4305 (---*--) |

|overweig 58 3.0360 0.5461 (-----*-----) |

|underwei 17 2.7247 0.4505 (----------*----------) |

|-----+---------+---------+---------+- |

|Pooled StDev = 0.4629 2.60 2.80 3.00 3.20 |

If (1, (2 and (3 are the population means of GPA for the about right, overweight and underweight groups, respectively, then the research hypotheses tested by this analysis is:

A) At least two of (1, (2 and (3 are different from each other.

B) (1, (2 and (3 are all different.

C) (1 = (2 ( (3

D) (1 > (2 > (3

7. A statistical test is done to compare the mean nose lengths of men and women and the p-value is 0.225. The hypothesis test is conducted using α=.05. Which of the following is the appropriate way to state the conclusion?

A) The mean nose lengths of the populations of men and women are identical.

B) Men have a greater mean nose length.

C) The probability is 0.225 that men and women have the same mean nose length.

D) There is not enough evidence to say that that the populations of men and women have different mean nose lengths.

8. In a two-factor ANOVA for which there are 3 levels of factor A, 5 levels of factor B, and 2 observations on each treatment, there are

A) 12 degrees of freedom for the error sources of variation.

B) 16 degrees of freedom for the error sources of variation.

C) 15 degrees of freedom for the error sources of variation.

D) 29 degrees of freedom for the error sources of variation.

9. In single-factor ANOVA, MSE is the mean square for error, and MSTr is the mean square for treatments. Which of the following statements are not true?

A) The value of MSTr is affected by the status of [pic] (true or false)

B) When [pic]is true, E(MSTr) = E(MSE) = [pic]is the common population variance.

C) When [pic]is false, E(MSTr) > E(MSE) = [pic]is the common population variance.

D) The value of MSE is affected by the status of [pic] (true or false).

Questions 10 to 11: A study compared testosterone levels among athletes in four sports: soccer, track, Lacrosse, and water polo. The total sample size was n =30 (10 soccer, 10 track, 5 Lacrosse, and 5 water polo). A one-way analysis of variance was used to compare the population mean levels for the four sports.

10. What are the numerator and denominator degrees of freedom for the F-test?

A) 10 for numerator and 30 for denominator.

B) 3 for numerator and 29 for denominator.

C) 3 for numerator and 26 for denominator.

D) None of the above.

11. The sum of squared errors is SS Error = 100. What is the value of the Mean Square Error (MS Error)?

A) 10

B) 3.45

C) 3.85

D) None of the above.

12. The abstinence rates at 12 months were 15.6 percent in the placebo group, as compared with 16.4 percent in the nicotine patch group, 30.3 percent in the bupropion group, and 35.5 percent in the group given bupropion and the nicotine patch. One group received a placebo. Why not just give this group no treatment at all?

A) It is not ethical to give no treatment at all in this setting.

B) Just thinking you are getting a treatment may have an effect, and we want to see if the real treatments do better than this.

C) A placebo is the same thing as no treatment at all.

D) Subjects would be disappointed if not given a pill.

13. An observational study has found that drivers who report that they routinely wear a seatbelt were less likely to have been given a traffic ticket for speeding in the past three years. Of the following, which is the most likely explanation for this observed relationship?

A) Police are less likely to stop a driver for speeding when they can see that he or she is wearing a seatbelt.

B) People are less likely to speed when they are wearing a seatbelt.

C) Confounding variables such as age and attention to risk factors in driving cause the same drivers who are likely to wear seatbelts to also be less likely to speed.

D) Relying on memory has created a problem because most people don't remember if they have had a speeding ticket in the past three years.

14. An experiment was done by randomly assigning each participant either to walk for half an hour three times a week or to sit quietly reading a book for half an hour three times a week. At the end of a year the change in participants' blood pressure over the year was measured, and the change was compared for the two groups. This is an experiment rather than an observational study because:

A) Blood pressure was measured at the beginning and end of the study.

B) The two groups were compared at the end of the study.

C) The participants were randomly assigned to either walk or read, rather than choosing their own activity.

D) A random sample of participants was used.

15. An experiment is usually preferred to an observational study because

A) One can draw a cause and effect conclusion in an experiment but not in an observational study.

B) It is easier to collect data from an experiment than it is from an observational study.

C) It is cheaper to run an experiment than it is to do an observational study.

D) Volunteers can be used for an experiment but not for an observational study.

16. Researchers would like to compare meditation and exercise to see which is more effective for reducing stress. One hundred people who suffer from high stress volunteer to participate in a study for ten weeks. Participants will either be given a 10-week course in meditation or will participate in a 10-week exercise program. The researchers must decide whether to randomly assign the volunteers to the two programs, or allow them to choose. Which of the following is the main advantage of randomly assigning participants to the two programs rather than allowing them to choose?

A) The participants are more likely to stick with the program for the full 10 weeks.

B) Confounding variables, such as past practice of meditation, should be approximately equal for the two groups.

C) Random assignment will allow the results to be extended to the population of all adults.

D) All of the above

Problems 1-4: Use α=.05 in analyzing the data. Attach SAS output to your answer sheets. If any assumptions are not satisfied, just note this in your write-up. It is not necessary to make efforts to remedy the problem(s). Each problem is worth 13 points.

1. High energy costs have made customers and home builders increasingly aware of whether household appliances are energy efficient. A large developer carries out a study to compare electricity usage for four different residential air-conditioning systems being considered for tract homes. Each system was installed in five homes, and the resulting electricity usage (in kilowatt-hours) was monitored for a 1-month period. Because the developer realized that many characteristics of a home could affect usage (e.g., floor space, type of insulation, directional orientation, and type of rood and exterior), care was taken to ensure that extraneous variation in such characteristics did not influence the conclusions. Homes selected for the experiment were separated into five groups consisting of four homes each in such a way that the four homes within any given group were as similar as possible. The resulting data appear below.

Group

|Air Conditioning System |1 |2 |3 |4 |5 |

|1 |116 |118 |97 |101 |115 |

|2 |171 |131 |105 |107 |129 |

|3 |138 |131 |115 |93 |110 |

|4 |144 |141 |115 |93 |99 |

2. A comparison of four diets records the number of pounds lost by each patient (Y) and a covariate, the initial weight of each patient (X). The data are found in the table below. Do the data provide sufficient evidence of differences among the adjusted treatment means?

Diet

1 2 3 4

|Pounds Lost |Initial Weight |Pounds Lost |Initial Weight |Pounds Lost |Initial Weight |Pounds Lost |Initial Weight |

|20 |215 |16 |230 |18 |206 |31 |251 |

|17 |220 |21 |219 |27 |239 |22 |223 |

|10 |180 |13 |210 |17 |188 |25 |250 |

|11 |196 |16 |211 |25 |240 |25 |243 |

|23 |217 |18 |236 |20 |210 |18 |192 |

|19 |201 |15 |220 |19 |222 |26 |239 |

3. Ten subjects agreed to participate in a study to examine the concentration of drug in the bloodstream for two different dosage forms (capsule and tablet) of the same product following a single dose. Presumably, within limits, the higher the concentration, the more effective the drug product. Five subjects were allocated at random to the capsule form and the other five to the tablet form. Subjects fasted from 8:00pm of the night prior to starting the study until 4 hours following ingestion of the assigned dose form (at 8:00 A.M. of the next day). Blood samples (15mL) were obtained at .5, 1, 2, 3, and 4 hours after dosing, and were analyzed for the concentration of the drug product in the bloodstream. The data (in ng/mL) are shown here.

Tablet Time Capsule Time

|Subject |.5 |1 |2 |3 |

|1 |204 205 |205 210 |203 204 |205 203 |

|2 |205 207 |205 206 |206 204 |209 207 |

|3 |211 209 |207 210 |209 214 |215 212 |

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