PSY315 week 2 worksheet complete solutions correct answers key

PSY315 week 2 worksheet complete solutions correct answers key

University of Phoenix Material                  

Practice Worksheet

Prepare a written response to the following questions.

Chapter 3

1.     For the following scores, find the mean, median, and the mode.  Which would be the most appropriate measure for this data set?

2, 2, 0, 5,1, 4,1, 3, 0, 0, 1, 4, 4, 0,1, 4, 3, 4, 2, 1

2.     Based on the scale of measurement for each variable listed below, which measure of central tendency is most appropriate for describing the data?

1. The time (in years) it takes a sample of students to graduate college

1. The blood type (e.g., Type A, B, AB, O) of a group of participants

1. The rankings of college undergraduate academic programs

3.     An expert reviews a sample of 10 scientific articles (n = 10) and records the following numbers of error in each article: 0, 4, 2, 8, 2, 3, 1, 0, 5, and 7. Compute the SS, the variance, and the standard deviation for this sample using the definitional and computational formulas.

4.     A psychologist interested in political behavior measured the square footage of the desks in the official office for four U.S. governors and of four chief executive officers (CEOs) of major U.S. corporations. The figures for the governors were 44, 36, 52, and 40 square feet. The figures for the CEOs were 32, 60, 48, 36 square feet.

a.     Figure the means and standard deviations for the governors and CEOs.

b.    Explain, to a person who has never had a course in statistics, what you have done.

c.     Note the ways in which the means and standard deviations differ, and speculate on the possible meaning of these differences, presuming that they are representative of U.S. governors and large corporations’ CEOs in general.
 

5.     Radel and colleagues (2011) conducted a study of how feeling overly controlled makes you desire—even unconsciously—more freedom. In their study, 52 Canadian undergraduates played a video game in a laboratory and were randomly assigned to either:

a.     an automony deprivation condition, in which they were told to follow instructions precisely, constantly given instructions over a loudspeaker, and carefully observed on everything they did.

b.    a neutral condition, which was much more laid back.
 

After this activity, they were asked to do a “lexical decision task” (a standard approach for measuring unconscious responses) in which they were shown a series of words and nonwords in random order and had to press “C” if it was a real word or “N” if not. Half of the real words were related to autonomy (e.g., freedom, choice) and half were neutral (e.g., whisper, hammer). The key focus of the study was on how long it took people to press the button *(“response latency”) for each kind of real word, averaged over the many words of each type. The table below shows the mean and standard deviation across the participants of these four categories of results. Thus, for example, 782 milliseconds (thousandths of a second) is the average time it took participants in the autonomy-deprived condition to respond to the autonomy-related words, and 211 is the standard deviation across the 26 participants’ average response time in that condition. Explain the numbers in this table to a person who has never had a course in statistics. (Be sure to explain some specific numbers, as well as the general principle of the mean and standard deviation.) For your interest, the pattern of results shown here supported the researchers’ hypothesis: “Relative to a neutral instructional climate, a controlling climate thwarting the need for autonomy…enhanced accessibility for autonomy-related words.” (p.924).

Mean Latencies (in Milliseconds) in the Lexical Task Assessing Accessibility for Autonomy-Related Constructs (Experiment 1)

Condition

Autonomy Deprivation

Neutral

Construct

M

SD

M

SD

Autonomy-related words

782

211

857

243

Neutral words

835

258

841

301

6.     On a standard measure of hearing ability, the mean is 300 and the standard deviation is 20. Give the Z scores for persons whose raw scores are 340, 310, and 260. Give the raw scores for persons whose Z scores on this test are 2.4, 1.5, and -4.5.
 

7.     Using the unit normal table, find the proportion under the standard normal curve that lies to the right of each of the following:
 

a.     z = 1.00

b.    z = -1.05

c.     z = 0

d.    z = 2.80

e.     z = 1.96

8.     Suppose that the scores of architects on a particular creativity test are normally distributed. Using a normal curve table (page 477-480), what percentage of architects have Z scores:
 

a.     Above .10?

b.    Below .10?

c.     Above .20?

d.    Below .20?

e.     Above 1.10?

f.     Below 1.10?

g.    Above -.10?

h.     Below -.10?

9.     A statistics instructor wants to measure the effectiveness of his teaching skills in a class of 102 students (N =102). He selects students by waiting at the door to the classroom prior to his lecture and pulling aside every third student to give him/her a questionnaire.

1. Is this sample design an example of random sampling? Explain.
2. Assuming that all students attend his class that day, how many students will he select to complete his questionnaire?

10.  Suppose that you were going to conduct a survey of visitors to your campus. You want the survey to be as representative as possible.

a.     How would you select the people to survey?

b.    Why would that be your best method?

11.  List the four steps of hypothesis testing, and explain the procedure and logic of each.
 

12.  Based on the information given for the following studies, decide whether to reject the null hypothesis. Assume that all populations are normally distributed. For each, give:    
 

d.    The Z-score cutoff (or cutoffs) on the comparison distribution at which the null hypothesis should be rejected.

e.     The Z-score on the comparison distribution for the sample score.

f.     Your conclusion.
 

Study

µ

σ

Sample
Score

p

Tails of Tests

A

5

1

7

0.05

1 (high predicted)

B

5

1

7

0.05

2

C

5

1

7

0.01

1 (High predicted)

D

5

1

7

0.01

2

13.  A researcher predicts that listening to music while solving math problems will make a particular brain area more active. To test this, a research participant has her brain scanned while listening to music and solving math problems, and the brain area of interest has a percentage signal change of 58. From many previous studies with this same math problem’s procedure (but not listening to music), it is known that the signal change in this brain is normally distributed with a mean of 35 and a standard deviation of 10.
 

a.     Using the .01 level, what should the researcher conclude? Solve this problem explicity using all five steps of hypothesis testing, and illustrate your answer with a sketch showing the comparison distribution, the cutoff (or cutoffs), and the score of the sample on this distribution.

Explain your answer to someone who has never had a course in statistics (but who is familiar with mean, standard deviation, and Z scores).
 

14. Two boats, the Prada (Italy) and the Oracle (USA), are competing for a spot in the upcoming America’s Cup race. They race over a part of the course several times. The sample times in minutes for the Prada were: 12.9, 12.5, 11.0, 13.3, 11.2, 11.4, 11.6, 12.3, 14.2, and 11.3.  The sample times in minutes for the Oracle were: 14.1, 14.1, 14.2, 17.4, 15.8, 16.7, 16.1, 13.3, 13.4, 13.6, 10.8, and 19.0. For data analysis, the appropriate test is the t-Test: Two-Sample Assuming Unequal Variances.
 

The next table shows the results of this independent t-test. At the .05 significance level, can we conclude that there is a difference in their mean times? Explain these results to a person who knows about the t test for a single sample but is unfamiliar with the t test for independent means.

Hypothesis Test: Independent Groups (t-test, unequal variance)

Prada

Oracle

12.170

14.875

mean

1.056

2.208

std. dev.

10

12

n

16

df

-2.7050

difference (Prada - Oracle)

0.7196

standard error of difference

0

hypothesized difference

-3.76

 t

.0017

 p-value (two-tailed)

-4.2304

confidence interval 95.% lower

-1.1796

confidence interval 95.% upper

1.5254

margin of error

15.  The Willow Run Outlet Mall has two Haggar Outlet Stores, one located on Peach Street and the other on Plum Street. The two stores are laid out differently, but both store managers claim their layout maximizes the amounts customers will purchase on impulse. A sample of ten customers at the Peach Street store revealed they spent the following amounts more than planned: $17.58, $19.73, $12.61, $17.79, $16.22, $15.82, $15.40, $15.86, $11.82, $15.85. A sample of fourteen customers at the Plum Street store revealed they spent the following amounts more than they planned when they entered the store: $18.19, $20.22, $17.38, $17.96, $23.92, $15.87, $16.47, $15.96, $16.79, $16.74, $21.40, $20.57, $19.79, $14.83. For Data Analysis, a t-Test: Two-Sample Assuming Unequal Variances was used.
 

At the .01 significance level is there a difference in the mean amount purchased on an impulse at the two stores? Explain these results to a person who knows about the t test for a single sample but is unfamiliar with the t test for independent means.

Hypothesis Test: Independent Groups (t-test, unequal variance)

Peach Street

Plum Street

15.8680

18.2921

mean

2.3306

2.5527

std. dev.

10

14

n

20

df

-2.42414

difference (Peach Street - Plum Street)

1.00431

standard error of difference

0

hypothesized difference

-2.41

 t

.0255

 p-value (two-tailed)

-5.28173

confidence interval 99.% lower

0.43345

confidence interval 99.% upper

2.85759

  margin of error

16.  Fry Brothers heating and Air Conditioning, Inc. employs Larry Clark and George Murnen to make service calls to repair furnaces and air conditioning units in homes. Tom Fry, the owner, would like to know whether there is a difference in the mean number of service calls they make per day. Assume the population standard deviation for Larry Clark is 1.05 calls per day and 1.23 calls per day for George Murnen. A random sample of 40 days last year showed that Larry Clark made an average of 4.77 calls per day. For a sample of 50 days George Murnen made an average of 5.02 calls per day. At the .05 significance level, is there a difference in the mean number of calls per day between the two employees? What is the p-value?

Hypothesis Test: Independent Groups (t-test, pooled variance)

Larry

George

4.77

5.02

mean

1.05

1.23

std. dev.

40

50

n

88 

df

-0.25000

difference (Larry - George)

1.33102

pooled variance

1.15370

pooled std. dev.

0.24474

standard error of difference

0

hypothesized difference

-1.02

 t

.3098

 p-value (two-tailed)

-0.73636

confidence interval 95.% lower

0.23636

confidence interval 95.% upper

0.48636

  margin of error

17.  A consumer organization wants to know if there is a difference in the price of a particular toy at three different types of stores. The price of the toy was checked in a sample of five discount toy stores, five variety stores, and five department stores. The results are shown below.

Discount toy

Variety

Department

$12

15

19

13

17

17

14

14

16

12

18

20

15

17

19

An ANOVA was run and the results are shown below.  At the .05 significance level, is there a difference in the mean prices between the three stores? What is the p-value?  Explain why an ANOVA was used to analyze this problem.

One factor ANOVA

Mean

n

Std. Dev

13.2

5

1.30

Discount Toys

16.2

5

1.64

Variety

18.2

5

1.64

Department

15.9

15

2.56

Total

ANOVA table

Source

SS

   df

MS

F

   p-value

Treatment

63.33

2

31.667

13.38

.0009

Error

28.40

12

2.367

Total

91.73

14

18.  A physician who specializes in weight control has three different diets she recommends. As an experiment, she randomly selected 15 patients and then assigned 5 to each diet. After three weeks the following weight losses, in pounds, were noted. At the .05 significance level, can she conclude that there is a difference in the mean amount of weight loss among the three diets?

Plan A

Plan B

Plan C

5

6

7

7

7

8

4

7

9

5

5

8

4

6

9

An ANOVA was run and the results are shown below.  At the .01 significance level, is there a difference in the weight loss between the three plans? What is the p-value?  What can you do to determine exactly where the difference is?

One factor ANOVA

Mean

n

Std. Dev

5.0

5

1.22

Plan A

6.2

5

0.84

Plan B

8.2

5

0.84

Plan C

6.5

15

1.64

Total

ANOVA table

Source

SS

   df

MS

F

   p-value

Treatment

26.13

2

13.067

13.52

.0008

Error

11.60

12

0.967

Total

37.73

14

19.  Your research team has been tasked with finding the correlation of the following scenario:

Four research participants take a test of manual dexterity (high scores mean better dexterity) and an anxiety test (high scores mean more anxiety). The scores are as follows:

Person                          Dexterity                       Anxiety

1                                  1                                  10

2                                  1                                    8

3                                  2                                    4

4                                  4                                  -2

Describe the process that your research team would go through by completing the following:

1. Make a scatter diagram of the scores. Should be negative direction
2. Describe in words the general pattern of correlation, if any.
3. Figure the correlation coefficient.
4. Explain the logic of what you have done, writing as if you are speaking to someone who has never heard of correlation (but who does understand the mean, standard deviation, Z scores, and hypothesis testing).
5. Give three logically possible directions of causality, indicating for each direction whether it is a reasonable explanation for the correlation in light of the variables involved (and why).