# STAT 300 Sample Midterm Exam 2015

Question

STAT 300 Sample Midterm Exam

Problem 1 (11 pts). Circle the answer which is the closest to the correct answer (choose

one answer only, unless indicated otherwise).

1. (3 pts) In a hypothesis testing, the power of the test does not depend on

(a) the specific alternative

(b) the sample size

(c) the p-value

(d) the test statistic being used.

2. (3 pts) The Chi-Squared test may perform poorly if

(a) the model does not hold

(b) the sample size is too small

(c) the conditions for the central limit theory do not hold

(d) none of the above

3. (5 pts) A new medication designed to reduce fever is being tested for efficacy and side

effects. For convenience, we call this new medication Drug X. The researcher wants to

test whether Drug X is more effective than the currently existing Drug Y. The experiment

enrolls 1200 patients (600 men and 600 women) with high fever. The primary outcome

measure is the drop in body temperature 3 hour after taking the treatment. The 1200

patients were first divided in two groups based on gender, then subjects within each

group are randomly assigned to the two treatment groups (Drug X and Drug Y). The

study included which of the following (select all that apply. You will lose 1 pt for each

wrong answer ):

(a) Blinding

(b) Randomization

(c) Blocking

(d) A placebo

(e) Missing values

1

Problem 2 (10 pts). A soft drink company has invented a new drink, and would like to

find out if it will be as popular as the existing favorite drink. For this purpose, its research

department arranges 7 participants for taste testing. Each participant tries the new drink and

rates it on a 5-point scale (1= terrible, …, 5 = excellent). The ratings are:

2 5 3 4 1 4 5

The company will sell the new drink if the median rating is at least 3. Fill the following

blanks as appropriate:

(a) (4 pts) Under the null hypothesis, the test statistic follows a Bin(n=7, p=0.5) distribution

(clearly specify the parameter values or degrees of freedom as appropriate).

(b) (3 pts) Is the hypothesis test one-sided or two-sided?

(c) (3 pts) Is a large sample required for the null distribution of the test statistic to be

reasonably accurate? (Yes or No).

Problem 3 (17 pts). Creed et al. describe a study in which patients with severe irritable

bowel syndrome (IBS) were randomly allocated to one of three treatment groups. One group

received eight hours of psychotherapy, one group was placed on a course of the antidepressant

Paroxeline while the third received the standard treatment (routine care by a gastroenterologist

or general practitioner). Subjects were assessed at the start of the trial and one year after the

end of treatment. One outcome measured was the number of days with “restricted activity” in

the year following the treatment. Suppose a sample of the data for this response were as below:

Psychotherapy 122 20 125 67 99

Paroxeline 100 180 75 127 118 222

Standard 54 216 127 208 166 355

1. (3 pts) For this study, which of the following methods could be the most appropriate to

test a suitable null hypothesis using the data?

(a) Two–sample t-test

(b) Wilcoxon Rank Sum test

(c) Kruskal-Wallis test

(d) Signed Rank test

(e) ANOVA

2

2. For the test you have selected:

(a) (3 pts) State the null hypothesis clearly in words (in one sentence).

(b) (3 pts) State the alternative hypothesis clearly in words (in one sentence).

Problem 4 (10 pts). Many statistical methods assume that the data follow Normal distributions.

In practice, this Normality assumption should be checked before applying the methods.

1. (6 pts) Name three statistical methods/models which rely on Normality assumptions for

the data. (If you name more than three, you lose two points for each wrong answer).

2. (4 pts) Suggest a method to check whether data follow a Normal distribution, and use

one sentence to briefly describe the method.

Problem 5 (17 pts). To investigate a possible association between two types of chemotherapy

drugs and the recurrence of a certain type of cancer, a total of 400 cancer patients were

randomly selected for a study. Half of the sample received treatment with Drug A, the remaining

half was treated with Drug B. After one year of follow-up for all individuals, the disease

had recurred in 25 people. Based on the collected data, individuals treated with Drug A were

four times as likely to experience recurrence compared to patients treated with Drug B.

1. (6 pts) Use the information to complete a contingency table, clearly labelling your rows

and columns and providing marginal totals.

Recurrence

Yes No Total

Drug A 20 180 200

Drug B 5 195 200

Total 25 375 400

or

Drug A Drug B Total

Recurred 20 5 25

Not recurred 180 195 375

Total 200 200 400

2. (3 pts) State the null hypothesis clearly in words (in one sentence).

4. (4 pts) After computing expected counts for all four cells, a test statistic with value 1.82 is

obtained. The 95-th percentile of the null distribution of this test statistic is 3.84. What

conclusion do you draw?

Explain your conclusion in words, in the context of this problem.

Problem 6 (10 pts). Suppose that the cancer recurrence under drug C is 10% based on

previous studies. A researcher wishes to check if the cancer recurrence rate has increased in

recent years. He designed a new experiment, collected a sample of 20 patients, and decided to

reject previous conclusion (i.e., 10% recurrence rate) if the observed recurrence percentage is

more than 20%.

Note: In both problems below, you only need to write down the mathematical equations to

calculate the desired probability or the sample size n without actually solving the equation. (i.e.,

you only need to show the methods, and you do not need to compute the final answers. Also,

either an approximate method or an exact method would be fine.)

1. (5 pts) What is the type I error probability based on the decision rule the researcher uses?

You only need to show the method without doing the calculations.

2. (5pts) The researcher wishes to have 80% power to detect a possible 15% recurrence rate.

How many data should he collect (i.e., what should be the sample size n)? Again, you

only need to show the method without doing calculations.

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