Exam 8: Introduction to the T Test: Single Sample and Dependent Means

An industrial researcher is a consultant to a large chain of bookstores. Industry reports show that for book stores in general, the average number of complaints received by management for a 1-month period at this time of year is 6.5 (the variance is not known). Seven of this chain's stores are randomly selected to keep records of complaints received over a 1-month period. The numbers of complaints are 4, 8, 9, 0, 3, 5, and 6. Does this chain get a different amount of complaints than book stores in general? (Use the .05 level). a. Use the five steps of hypothesis gathering. b. Explain what you did to a person who is familiar with hypothesis testing with a known population variance and a single sample, including understanding decision errors, effect size, and power, but knows nothing about t tests of any kind.

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Question 1

Correct Answer:

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Step 1 (some version of the following is acceptable):
• Pop I: Seven of the chain's bookstores selected to keep records; Pop 2: Bookstores in general
• Research Hypothesis: Pop I gets a different amount of complaints than bookstores in general (Pop I not equal to Pop II); Null Hypothesis: Pop I = Pop 2
Step 2 (determine the characteristics of the comparison distribution):
• The comparison distribution is a distribution of means, but the population variance is unknown and must be estimated from the sample
• The mean is the same as the known population mean = 6.5 complaints
• We will use a t distribution with 6 degrees of freedom
• Estimated population variance = 56 / 6 = 9.33
• Variance of distribution of means = 9.33 / 7 = 1.33
• SD of distribution of means = sqroot of 1.33 = 1.15
Step 3 (determine cutoff sample score on the comparison distribution at which we'll reject H₀):
• Two-tailed test at .05 level, use t table to determine cutoff value of ±2.447
Step 4 (determine your sample's score on the comparison distribution):
• t = 5-6.5 / 1.15 = -1.30
Step 5 (decide whether to reject the null hypothesis):
• Do not reject. The randomly selected bookstores from this large chain do not receive more complaints than bookstores in general-results are inconclusive.

You obtain pretest and posttest scores from a group of participants. Before conducting a t test for dependent means, you first combine the two sets of scores into one set of scores by figuring __________.

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Question 2

Correct Answer:

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difference scores, change scores

Approximately how many research participants would be required for 80% power for a study using the t test for dependent means (assume a two-tailed hypothesis with an expected small effect size of .20):

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Question 3

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If a sample has 27 people in it, the degrees of freedom used in the formula to estimate the population variance would be:

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Question 4

For the following question(s): Professor Juarez thinks the students in her statistics class this term are more creative than most students at this university. A previous study found that students at this university had a mean score of 35 on a standard creativity test. Professor Juarez finds that her class scores an average of 40 on this scale, with an estimated population standard deviation of 7. The standard deviation of the distribution of means comes out to 1.63. -What is the t score?

(Multiple Choice)

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Question 5

Suppose the counselor tested the null hypothesis that fourth graders in this class were less depressed than those at the school generally. She figures her t score to be -.20. What decision should she make regarding the null hypothesis?

(Multiple Choice)

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Question 6

Power for a t test for dependent means can be determined using a power software package, Internet power calculator, or power table. (True or False)

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Question 7

In a study the sum of squared deviations from the mean for the sample is 12 and there are 4 participants. What is the estimated population variance?

(Short Answer)

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Question 8

A t distribution looks to the eye like the normal curve, but differs subtly in having slightly _________ scores at the extreme. (more or less)

(Short Answer)

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Question 9

What is the main difference between Z score and t score?

(Multiple Choice)

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Question 10

An organizational specialist is hired as a consultant to a company planning to open a coffee house for college students. The company wants to know if the customers will drink more coffee if the coffee house is decorated in a Paris motif or in a San Francisco motif. To test this, the researcher sets up two similar rooms, but with the two different motifs. She then arranges to have eight students spend an afternoon in each room while being allowed to drink all the coffee they like. (The order in which they sit in the rooms is rotated, so that half do their first afternoon in the Paris room and half in the San Francisco room.)The amount each student drinks is recorded below: Cups of Coffee Consumed for each Motif Is there is' a significant difference between the number of cups of coffee consumed in the two rooms? a. Use the five steps of hypothesis testing (at the .05 level of significance) b. Figure the effect size and find the approximate power of this study

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Question 11

A research article reports results of a study using a t test for dependent means as "t(16)= 2.67, p < .05." This tells you:

(Multiple Choice)

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Question 12

For the following question(s): Professor Juarez thinks the students in her statistics class this term are more creative than most students at this university. A previous study found that students at this university had a mean score of 35 on a standard creativity test. Professor Juarez finds that her class scores an average of 40 on this scale, with an estimated population standard deviation of 7. The standard deviation of the distribution of means comes out to 1.63. -What effect size did Professor Juarez find?

(Multiple Choice)

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Question 13

The estimate of a population parameter that is likely systematically to overestimate or underestimate the true value of the population parameter is known as a __________.

(Short Answer)

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Question 14

In a study with 15 degrees of freedom, what would be your cutoff score for a t distribution using a two-tailed test at the .01 level of significance?

(Multiple Choice)

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Question 15

For the following question(s): A researcher conducts a t test for dependent means in which it is predicted that there will be a decrease in unemployment from before to after a particular job-skills training program. The cutoff t needed is -1.833. The standard deviation of the distribution of means of change scores is 2.0 and the mean change score for the sample studied is an increase of 5.2. -What is the appropriate conclusion?

(Multiple Choice)

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Question 16

Which of the following is an assumption or requirement within the logic and mathematics of the t test?

(Multiple Choice)

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Question 17

The variance of a sample is a(n)__________ estimator of the population variance.

(Short Answer)

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Question 18

In the formula for estimating the population variance from the scores in a sample, the sum of squared deviations is divided by:

(Multiple Choice)

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Question 19

A sample has individuals with scores of 1, 3, 5, 6, and 6. What is the estimated population variance?

(Multiple Choice)

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Question 20

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You obtain pretest and posttest scores from a group of participants. Before conducting a t test for dependent means, you first combine the two sets of scores into one set of scores by figuring __________.

Approximately how many research participants would be required for 80% power for a study using the t test for dependent means (assume a two-tailed hypothesis with an expected small effect size of .20):

If a sample has 27 people in it, the degrees of freedom used in the formula to estimate the population variance would be:

Suppose the counselor tested the null hypothesis that fourth graders in this class were less depressed than those at the school generally. She figures her t score to be -.20. What decision should she make regarding the null hypothesis?

Power for a t test for dependent means can be determined using a power software package, Internet power calculator, or power table. (True or False)

In a study the sum of squared deviations from the mean for the sample is 12 and there are 4 participants. What is the estimated population variance?

A t distribution looks to the eye like the normal curve, but differs subtly in having slightly _________ scores at the extreme. (more or less)

What is the main difference between Z score and t score?

A research article reports results of a study using a t test for dependent means as "t(16)= 2.67, p < .05." This tells you:

The estimate of a population parameter that is likely systematically to overestimate or underestimate the true value of the population parameter is known as a __________.

In a study with 15 degrees of freedom, what would be your cutoff score for a t distribution using a two-tailed test at the .01 level of significance?

Which of the following is an assumption or requirement within the logic and mathematics of the t test?

The variance of a sample is a(n)__________ estimator of the population variance.

In the formula for estimating the population variance from the scores in a sample, the sum of squared deviations is divided by:

A sample has individuals with scores of 1, 3, 5, 6, and 6. What is the estimated population variance?

Displaying the Order in a Group of Numbers Using Tables and Graphs

The Mean, Variance, Standard Deviation, and Z Scores

Correlation and Prediction

Some Key Ingredients for Inferential Statistics: the Normal Curve, Sample Versus Population, and Probability

Introduction to Hypothesis Testing

Hypothesis Tests With Means of Samples

Making Sense of Statistical Significance: Effect Size and Statistical Power

The T Test for Independent Means

Introduction to the Analysis of Variance

Chi-Square Tests and Strategies When Population Distributions Are Not Normal

Applying Statistical Methods in Your Own Research Project

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