Multiple Choice Section (1 point each, 200 points total)

1. For a sample of size 20 taken from a normally distributed population with standard deviation equal 5, a 90% confidence interval for the population mean would require the use of:
   1. a. t = 1.328 b. t = 1.729 c. χ2 = 11.6509 d. z = 1.645
2. For the set of numbers {11, 17, 14, 10, 13, 8, 7, 14}, the median location is __________, and the median is __________.
   1. 14, 12 b. 4.5, 12 c. 12, 14 d. 11.75, 14
3. In order to determine the p-value, which of the following is not needed?
   1. The level of significance b. Whether the test is one or two tail
      c. The value of the test statistic d. All of the above are needed
4. In a chi-squared test for a 5 by 3 contingency table:
   (a) variables must be qualitative
   (b) observed frequencies are compared to expected frequencies
   (c) there are 15 degrees of freedom
   (d) at least 12 cells must have expected values greater than 5
   (e) all the observed values must be greater than 1
5. A researcher is studying treatments for agoraphobia with panic disorder.  The treatments are to be the drug Imipramine at the two doses 1.5 mg per kg of body weight and 2.5 mg per kg of body weight.  There will also be a control group given a placebo.  Thirty patients were randomly divided into three groups of ten each.  One group was assigned to the control, and the other two groups were assigned to the two drug treatments.  The numerator degrees of freedom for the ANOVA F-test would be:

1. 2        b)  3          c)  27          d)  29

1. The power of a test is the probability of making:

1. A correct decision when the null hypothesis is false
2. A correct decision when the null hypothesis is true
3. Incorrect decision when the null hypothesis is false
4. Incorrect decision when the null hypothesis is true

1. In the equation =12.6 X + 5,
   1. a difference of one unit in X will lead to a 5-point difference in the prediction.
   2. will decrease as X increases.
   3. the correlation is certain to be significant.
   4. a difference of one unit in X is associated with a 12.6-point difference in the prediction.
2. The GLM (two factor ANOVA) is used to test statistical hypotheses concerning:
   1. variances. b. standard deviations c. means d. errors
      Short Answers
3. Identify what type of scale (nominal, ordinal or ratio) is being used, and select the measure of central tendency (mean, median or mode) that would be most appropriate for describing each of the following hypothetical sets of data. (1 point each)
   1. Heart rates for a group of women before they start their first aerobics class.
   2. Religious affiliation of delegates to the United Nations.
   3. Annual incomes of baseball players, with the highest category being "$1 million or more".
4. On average, do males outperform females in mathematics? To answer this question, psychologists at the GCU compared the scores of male and female eighth-grade students who took a basic skill math test. A summary of the test scores is displayed below.

   	Males	Females
   Sample Size	1764	1739
   Mean	48.9	48.4
   Standard Deviation	12.96	11.85

   
   Without carrying out any further calculations, what do you conclude? Why? (2 points)
5. A distribution has a mean of 50 and a median of 39. Is it this distribution is positively skewed or negatively skewed? Explain your answer briefly. (2 points)
6. A study was conducted to determine whether physically fit persons sleep more hours than those who are not physically fit. Two groups of people were selected. One group consisted of people who work out at least 3 times a week. The other group consisted of people that do not work out at all. For one week, subjects slept in a sleep lab and an experimenter recorded the number of hours each person slept.
   1. What is the independent variable? (1 point)
   2. What is the dependent variable? (1 point)
   3. Is the dependent variable discrete or continuous? Is it nominal, ordinal, interval, or ratio? (2 points)
   4. Is the independent variable discrete or continuous? Is it nominal, ordinal, interval, or ratio? (2 points)
7. What test should I use for the following? Where relevant, please indicate if I should use a one or a two sided (tailed) test? (2 points each)
   1. You want to test whether a new drug really improves the memory of Alzheimer's patients by testing them at recruitment time and again after 2 months of the drug treatment
   2. You want to test whether patients with Parkinson's, Huntington's or Alzheimer's have different frequencies of having a memory deficit
   3. A researcher thinks stress levels can be related to how long people have spent in cities. She surveys 100 people asking them how long each has lived in the city. She then carries out a test that provides a number describing the stress level for each.
   4. In a large corporation the mean entry level salary is $27,000. The entry level salaries for a random sample of 15 employees with only high school degrees is $24,100 with a standard deviation of 6,000. Do people with only high school degrees earn less than the rest of the company?
      
   5. You want to know whether how much fizz is in Coke, Pepsi, and RC.  You and a friend take a case of each to the roof of A& S and measure how far they spray onto the pavement below after a thorough shaking.
   6. You want to know whether Biology majors or P.E. Majors run faster.  You get a group of 20 Biology and 20 P.E. Majors together and have them run from A&S to the Apollo Fountain and back.  Unfortunately your stopwatch broke, so you only know who beat whom.
   7. You want to determine whether high self-esteem or open-mindedness (both scaled) is a better predictor of success in the corporate world (measured in annual salary).
8. A library system lends books for periods of 21 days. This policy is being reevaluated in view of a possible new loan period that could be either longer or shorter than 21 days. To aid in this decision a local researcher drew a random sample of loan records and found the following loan periods: 20, 16, 10, 24, 18, 21, 15, 16. By hand, and showing the necessary calculations, use a parametric test to determine whether the actual loan period differs from 3 weeks? (3 points)

1. By hand, and showing your calculations, please use a non-parametric test to test the same hypothesis. What do you conclude? (2 points)

1. The following temperatures were recorded in a rabbit various times after being introduced with rinderpest virus. We want to predict body temperature from knowing the time since infection of a rabbit.

1. By HAND SHOWING YOUR CALCULATIONS, what is formula for the best fit line for temperature from time after injection? (5 points)

B. What proportion of the variability is predicted by the line? (3 points)

C. Is there a significant relationship between the variables (test whether b = 0). Show your work! (3 points)

1. A plant ecologist wishes to test the hypothesis that the height of species X depends on the type of soil it grows in. She measures the height of 3 plants in each of 3different soil types. The results are tabulated below. (Height in centimeters.)

.

1. BY HAND AND SHOWING ALL OF YOUR WORK, please calculate the appropriate parametric test to assess whether or not the results support her hypothesis, assuming normality and equality of variances? (4 points)
2. By hand, and showing your work, please calculate a non-parametric test of the same hypothesis. What do you conclude? (3 points)

1. A psychologist would like to know how much difference there is between the problem-solving ability of 8-year-old children versus 10-year-old children. A random sample of 10 children is selected from each group. The children are given a problem-solving test, and the results are summarized as follows:

1. Determine whether the variances can be considered equal. Show your work please. (2 points)
2. Test the hypothesis that the problem-solving ability of 10 year olds is different from that of 8 year-olds. Again, please show your work (3 points)

1. On one pacific island that 34% of people have blood type A, 15% blood type B, 23% blood type AB, and 28% blood type O. We go out and collect a sample of blood from 100 people on an island at the other end of the archipelago, and find the following:
   A: 12 B: 56 AB: 2 O: 30
   1. Present the data that was collected by this researcher in an appropriate graphical form. Be sure to label your graph appropriately and to give it an appropriate title. (4 points)
   2. Calculating by hand, is our result compatible with the hypothesis that the distribution of blood groups is the same within the populations on both islands? Explain! (3 points)
      Mostly SPSS and Sigmaplot Section
2. A poll of 100 US. congress people was taken to determine their opinions concerning a bill to lift the ban on stem cell research. Each congressperson was then classified according to political party affiliation and opinion on the policy. The results are summarized below. Since the vote is close, one would like to find out whether congress voted along party lines or not. Therefore, please test the null hypothesis that these two classifications are independent of one another, against the alternative hypothesis that they are not. Use a level of significance of 0.05

1. Construct a contingency table for this data. (You may use SPSS if you wish!) (3 points)
2. What are the expected values for each cell (show calcs or annotated SPSS output please)? (3 points)
3. Is there independence between political standing and opinion on this issue? Explain! (3 points)

1. A health educator suspects that the "days of discomfort" caused by common colds can be reduced by ingesting large doses of vitamin C and visiting a sauna every day. Using a two-factor design, subjects with new colds are randomly assigned to one of four different daily doses of vitamin C (either 0, 500, 1000, or 1500 milligrams) and to one of three different daily exposures to a sauna (either 0, 0.5 or 1 hour). The number of days spent suffering from cold symptoms for each group are shown below.

1. Code your data and carry out the appropriate parametric analysis using SPSS. Choose descriptives and homogeneity of variance tests from the options menu and any post hoc tests you feel would be appropriate. Please provide me with your output and interpretation of it. (At least half the points are on interpretation, so please don’t skimp on this!) (4 points)
2. Do either (or both) of the treatments significantly reduce the number of days of discomfort? Explain! (3 points)
3. Is there a significant interaction between the two treatments? Explain. (2 points)
4. Whether or not there was an interaction in this specific case, please explain what an interaction would mean / have meant in this case. (i.e. if there was an interaction, what would this tell you?) 2 points.

1. On average, drug stores sell 47 bottles of "Fountain of Youth", a herbal remedy that is supposed to increase longevity, and promote youthful appearance in skin. However yesterday NBC aired a segment on "FOY" that suggested that the drug might reduce libido, increase appetite and may even promote symptoms of depression in some users. The next day you measure the sales in stores around the country and this is what you found (note: this is all one data set: the columns are just to save space!):

1. What are the null and alternative hypotheses for this study? (2 points)
2. Has the story affected sales? (You may use SPSS to answer this question. However if you do, please provide a copy of your output in which you indicate what pieces of the print out you used to reach your conclusion). (3 points)

1. Researchers have asked several smokers how many cigarettes they had smoked in the previous day. Here are the data.

1. Should you use a parametric or non-parametric test to analyze this data. Explain! (2 points)
2. Carry out an appropriate test to determine whether or not there is a difference between the mean number of cigarettes smoked per day between the sexes? Please show your work or provide a copy of your INTERPRETED SPSS output. (4 points)

1. Let’s say you carry out a study of memory-enhancing drugs on number of words in a list recalled an hour after study for pools of 8 volunteers each (total 32 volunteers). In the experiment you give 8 patients Drug 1, 8 other patients receive drug 2 and the final 8 patients drug 1 and 2 in combination. Here are your results:

1. Create an appropriate graph to compare these data, making sure to label your graph axes appropriately and to give it an appropriate title. (4 points)
2. Carry out the appropriate statistical analysis using SPSS to test whether the levels are different. Please provide me with your output and interpretation of it. (3 points)
3. Was the assumption of homogeneity of variance met? Explain (2 points)!
4. Using one or more post hoc tests, which means were different to which? (1 points)

1. An investigator feels that she may be able to recognize babies at risk from fetal alcohol syndrome due to the fact that they have lower birth weights than would be predicted from their mother’s pre-pregnancy weight. To establish this she must first determine whether there is a predictive relationship between a mother's weight and her infant's birth weight so she collects the following data:

1. Construct the appropriate type of graph for these data. Label the axes appropriately and provide an appropriate title for the graph. (4 points)
2. Using SPSS, analyze this data using the appropriate statistical test (3 points)
3. What is the value of r ² and what does this tell you? (2 points)
4. Is this better than would be expected by chance alone? Explain (2 points)
5. What is the formula for the line that describes the relationship between mother’s pre-pregnancy weight and infant birth weight? (Base formula is y = mx +b… what is m and what is b?) (3 points)
6. Use that formula to predict the birth-weight of a baby born to a woman weighing (i) 42kg (i) 75kg. (2 points)

1. A chicken pathologist compares testosterone levels in three strains of roosters. The data are:

Strain 1:  439  568  134  897   229   329
Strain 2:  103  115  098  126   115   120
Strain 3:  107  099  102  105   089   110

1. Create an appropriate graph to compare these data, making sure to label your graph axes appropriately and to give it an appropriate title. (4 points)
2. Carry out the appropriate statistical analysis using SPSS to test whether the levels are different. Please provide me with your output and interpretation of it. (4 points)
3. Was the assumption of homogeneity of variance met? Explain! (2 points)
4. Using one or more post hoc tests, which means were different to which? (3 points)

1. A researcher wants to understand factors that may influence plant species diversity in pingos (dry, alpine-like habitats that occur within extensive arctic wetlands). The variables are:

• Study area: One of four areas that are characterized by different surficial geology and somewhat different climates (a nominal variable).
• Type: One of two morphological types of pingos - a steep-sided classic form and a giant, broad-based form that we first described (an ordinal variable)
• Height : Height in m
• Diameter : Diameter in m
• Surface area: An estimate of surface area in m
• Mean pH: Mean pH of a series of soil samples
• SD of pH: Standard deviation of pH of a series of soil samples
• Distance to coast : Distance to the coast, in km, measured along the primary wind vector; this is very highly correlated with thawing-degree days and is therefore an indirect estimate of summer temperature
• Distance to nearest neighbor : Distance to the nearest pingo in km
• Distance to nearest river : Distance to the nearest river, in km
• Number of vascular species: Total number of vascular plant species (= a measure of diversity)

Carry out a multiple regression between the number of vascular plants and all of the independent factors.

Please provide me with a copy of your INTERPRETED SPSS output (3 points)

1. What is the value of r ² and what does this tell you? (2 points)
2. Is this better than would be expected by chance alone? Explain. (2 points)
3. Which factors appear to be the most powerful predictors of vascular plant diversity? (2 points)
4. What do the histogram and partial plots tell you about the appropriateness of this data set for this type of analysis? (2 points)

1. A research study was conducted to examine the clinical efficacy of a new antidepressant. Depressed patients were randomly assigned to one of three groups: a placebo group, a group that received a low dose of the drug, and a group that received a moderate dose of the drug. After four weeks of treatment, the patients completed the Beck Depression Inventory. The higher the score, the more depressed the patient. The data are presented below. Compute the appropriate test.

1. What type of test should you use to assess differences between these treatments and why? (2 points)
2. Run that test by hand or using SPSS, providing me with copies of your interpreted output. Are the survivorship times equal in the three groups? (4 points)

1. A single leaf is taken from 11 different tobacco plants. Each leaf is divided in half, and given one of two preparations of mosaic virus. We wish to examine if there is a difference in the mean number of lesions from the two preparations. Here is the raw data:

1. Run the appropriate statistical test and tell me what you conclude (please provide copies of your SPSS output edited with your comments and interpretation (4 points)

Bonus Question

The following file contains part of the data for a study of oral condition of cancer patients.  The oral conditions of the patients were measured and recorded at the initial stage, at the end of the second week, at the end of the fourth week, and at the end of the sixth week.  The variables age, initial weight and initial cancer stage of the patients were recorded.  Patients were divided into two groups:  One group received a placebo and the other group received aloe juice treatment. The variables in the data set are:

trt - treatment group:  0=placebo; 1=aloe juice

TOTALCIN - oral condition at the initial stage

TOTALCW2 – oral condition at the end of week 2

TOTALCW4 – oral condition at the end of week 4

TOTALCW6 – oral condition at the end of week 6

1. Is there a change in oral condition over time? Explain! 2 points.
2. Is there a difference in the nature of the change over time between the treatment and the control? Explain! 2 points.
3. Does the data set meet the sphericity assumption? Explain! 2 points.
4. Is there a treatment effect? Explain! 2 points.
5. What does the power analysis tell you about why you may have found the result you did in d? Explain! 2 points.

Solution: We need to perform a Repeated-Measures ANOVA:

• The table above shows that there is a change in oral condition over time (p = 0.000), and time doesn’t interact with the treatment.
• We have

which means that there is not a significant difference between treatment and control

• As we can observed, sphericity is met (p = 0.476):

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