Chapter 7 Testing Differences Between Means
Name ______TA ______Date: ______
PSYC105 Statistics
Spring 2011
Exam 2
Part 1. Multiple Choice (2 points each). Following are 21 multiple choice questions. Please circle the best answer and write it in the blank space. For each question, the best answer is the one that most comprehensively answers the question. Good luck!
______1) The alternative hypothesis:
A) is denoted by H0
B) states that the treatment does have an effect on the dependent variable
C) must be rejected if our test statistic is greater than our critical value
D) All of the above
______2) A Type II Error occurs when:
A)There is an effect, but the null hypothesis is rejected
B)There is no effect, and the null hypothesis is retained
C)There is an effect, but the null hypothesis is retained
D)There is no effect, and the null hypothesis is rejected
______3) When would you be most likely to conduct a one-tailed test (vs. a two-tailed test)?
A)If you have a strong prediction about the direction of the effect.
B)If you have a small sample size.
C)If you only have one sample (instead of two).
D)None of the above.
______4) A researcher is using data from a single sample to conduct a two-tailed hypothesis test. If n = 17, and α = .05, what are the critical values for a z-test and a t-test, respectively?
A) +/- 1.96 ; +/- 2.11
B) +/- 1.65; +/- 2.10
C) +/- 1.28; +/- 1.74
D) +/- 1.96; +/- 2.12
______5) Dr. Phil wants to assess the effectiveness of participation in his talk show on marital quality. The mean marital satisfaction score of the population of married couples in this country is 73, with a standard deviation of 12. In a sample of 36 couples who participated in his talk show, Dr. Phil finds an average marital satisfaction score of 79. What can Dr. Phil conclude? (Assume = .05, and a two-tailed test)
A)Dr. Phil’s talk show significantly increased marital satisfaction
B)Dr. Phil’s talk show significantly decreased marital satisfaction
C)Dr. Phil’s talk show significantly affected marital satisfaction, but it is impossible to tell whether it increased or decreased scores.
D)Dr. Phil’s talk show had no significant effect on marital satisfaction
______6) A particular test statistic yields the following effect sizes: Cohen’s d = .83, and r2 = .26. Based on the common criteria for evaluating these effect sizes, the first value (d) is best classified as a ______effect, and the second value (r2) is best classified as a ______effect.
A)large; small
B)medium; small
C)large; medium
D)large; large
_____7) Humphrey is looking for a gaming friend and wants to find out if people on the east coast spend more time playing video games than the general U.S. population. He collects data from a sample of east coast participants, which yields a mean of 7 hours per week, with a standard deviation of 2 hours. What is the effect size of Humphrey’s hypothesis test if the population mean in the general U.S. population is only 5 hours per week?
A)d = -1.5
B)d = 6.0
C)d = 2.5
D)d = 1.0
______8) As the alphalevel for a hypothesis test decreases, what happens to the chance that we will make a Type I Error (incorrectly reject the null hypothesis)?
A)Probability of a Type I Error increases
B)Probability of a Type I Error decreases
C)Probability of a Type I Error remains the same
D)Impossible to say given the information provided
_____ 9) A researcher is interested in how Clark students’ anxiety levels are affected by participating in her research study (the treatment). She is told that the average anxiety level for the population of the Clark student body is 100. She conducts a two-tailed hypothesis test to examine whether her treatment works. In conducting her research, what will be her null hypothesis (H0 )?
A)μtreatment = 100
B) μtreatment ≠100
C) μtreatment > 100
D) μtreatment > 100
______10) An intervention researcher whose experiment produced the following test statistic: t(24) = 2.32, p < .05 would most likely conclude what?
A)The intervention was unsuccessful; there is no significant difference between treatment and control groups
B)The intervention was unsuccessful; there is a significant difference between treatment and control groups
C)The intervention was successful; there is a significant difference between treatment and control groups
D)The intervention was successful; there is no significant difference between treatment and control groups
______11) The purpose of the effect size is to indicate the magnitude of the treatment effect, regardless of the ______.
A)mean
B)sample size
C)z-score
D)correlation
______12) If the sample data produce a test statistic (e.g., z-score) that is in the critical region, then which of the following is the appropriate conclusion for the hypothesis test?
A) reject H0
B) reject H1
C) fail to reject H0
D) fail to reject H1
_____ 13) Which set of sample characteristics is most likely to produce a significant t-statistic?
A) a small sample size and a small sample variance
B) a large sample size and a large sample variance
C) a large sample size and a small sample variance
D) a small sample size and a large sample variance
______14) In a two-tailed, single sample t-test (df = 22, α = .05), if the difference between the observed sample mean and the hypothesized (or expected) population mean is 30, and the estimated standard error of the mean is 15, what can we conclude about the null hypothesis?
A)It should be rejected
B)It should be retained
C)It cannot be tested
D)Not enough information to determine
______15) The following are the quantities of sugar found in 5 samples of each of two brands of soda:
Pepsi: 50mg 40mg 62mg 43mg
Coke: 38mg 57mg 44mg 53mg
Which of the following procedures is appropriate to test the hypothesis of equal average sugar content in the two types of soda?
A) Single sample t-test with 7 degrees of freedom
B) Independent samples t-test with 6 degrees of freedom
C) Independent samples t-test with 7 degrees of freedom
D) Paired samples t-test with 4 degrees of freedom
_____16). If the alpha level is increased, the size of the critical region______.
A)stays the same
B)increases
C)decreases
D)need more information to answer this question
_____17)For the following research question, which type of statistical procedure is most appropriate for a study on the effectiveness of a treatment program for recovering cocaine abusers?“Was there a significant difference in cocaine use between pretest and the post-test follow-up for the treatment group?”
A)Repeated measures t-test
B)Z-test
C)Independent samples t-test
D)Single samples t-test
______18) Which of the following is true of the t-distribution?
A)The t-distribution has less variability than the normal curve
B)The t-distribution always looks exactly like the normal curve
C)The t-distribution is skewed
D)Unlike the normal curve, the t-distribution changes depending on the sample size
______19) Which of the following is an advantage of the repeated measures design?
A)It allows for more attrition
B) It reduces the influence of individual differences on our treatment outcome
C) It allows us to recruit much bigger sample sizes
D) all of the above
______20) An independent-samplest-test:
A) uses a different sample for each of the different treatment conditions being compared.
B) uses pooled variance in the calculation of standard error.
C) uses the data from two samples to evaluate a hypothesis about the difference between two population means.
D) All of the above
______21) Jon is conducting a study on self-esteem. He wants to see whether there is a difference in self-esteem between a sample of males and a sample of females. What type of test should he conduct?
A)single-sample t-test
B)z-test
C)independent samples t-test
D)related samples t-test
Part II. For the following questions, you will be given a research scenario and asked to conduct the steps of hypothesis testing. Round all answers to two decimal places.
Refer to the following situation for questions 1-7 below.
A researcher at Central Hartford East and West University (CHEW U.) is testing out a new super long-lasting chewing gum. He knows that, on average, the population chews a piece of gum for a mean of µ = 18.8 minutes before spitting it out, but the variance and standard deviation of the population are unknown. A sample of n=9studentsis given the new long-lasting gum. Students in this sample chewed for an average of M = 21.0 minutes with standard deviation s = 2.4 minutes. Use a two-tailed test with α = .05.
1)State the null and alternative hypotheses (using words rather than symbols). (2 points)
2) What are the degrees of freedom for this test (2 points)?
3). What isthe critical value(s) for this hypothesis test? (2 points)
4) What is the estimated standard error? (3 points)
5) What is the value of the test statistic? (3 points)
6)Draw your conclusions. Can you reject the null hypothesis? Does this long-lasting chewing gum actually work? (4 points)
7) Compute and interpret Cohen’s d(small, medium, or large effect?) (3 points)
Refer to the following situation for questions 8-12 below.
A researcher at New England Western University (NEW U.) wants to determine whether a new exercise program affects weight loss. The population of students who did not participate in the program lost an average of µ = 300 grams per day with a standard deviation σ = 50. For a sample of n = 16 students who participated in the exercise program, the researcher found an average of M = 328grams lost per day. Use a two-tailed test with α = .05 to determine whether this exercise program was effective.
8)State the null and alternative hypotheses (using symbols rather than words). (2 points)
9)Find the critical value(s) for this hypothesis test.(2 points)
10) What is the standard error? (3 points)
11) What is the value of your test statistic? (3 points)
12)Draw your conclusions. Can you reject the null hypothesis? Is the exercise program effective in leading to weight loss? (4 points)
Refer to the following scenario for questions 14-21 below. (19 points total)
A researcher at Basin of Lower and Upper England University (BLUE U.) is obsessed with colors. He wants to examine whether wearing the color blue actually leads to better test performance. To test for group differences, the researcher randomly assigns students to two independent groups. One is the Experimental group (Group A) that is required to wear blue outfits to their next exam (the treatment). The other (Group B) is the control group that wears their normal clothes to the exam. Their scores on a 10-point test are presented below. Using an alpha level of .05 (two-tailed), determine whether the two groups differ in their test scores.
Group A (treatment)Group B (control)
6 4
7 2
5 5
43
66
M = 5.6M = 4.0
SS = 5.2SS = 10.0
14) State the null and alternative hypotheses (in both words and symbols). (4 points)
15) What are the degrees of freedom for the test statistic? (2 points)
16) What are the critical values for the test statistic (2 points)?
17) Calculate the pooled variance. (2 points)
18) Calculate the estimated standard error. (2 points)
19) Calculate the value of the test statistic(2 points)
20) Draw conclusions based on your obtained t-statistic. Can you reject the null hypothesis? Are there differences between the groups – if so, what are those differences? (4 points)
21) Calculate the percentage of variance explained (r2) and interpret this value (small, medium, or large effect?).(3 points)
Question #22 is a general question and does NOT refer to any of the particular examples on the exam.
22) Briefly(in one sentence or less) describe when you would use the following statistical tests (4 points)
Z-test:
Single Sample t-test:
Independent Samples t-test:
Repeated Measures t-test:
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