# Problem 1;Read the explanation given which also contains the questions

*label*Statistics

*timer*Asked: Apr 19th, 2017

**Question description**

PART A: Is it appropriate to use the two-sample *t*-procedures? Give reasons for your answer. Choose one correct answer.

A.Itisnotappropriatetousethetwo-sample -proceduressincethedistributionisnot Normal.

B.Itisnotappropriatetousethetwo-sample -proceduressincewecannotassess Normality without knowing the detailed data.

C.Theuseofthe -proceduresisappropriate,becausetheproximityofthemeansand standard deviations show that the two distributions are similar.

D.Assumethattherearenooutliers.The -proceduresshouldbeappropriate,becausewe have two large samples.

PART B : Let *m*1 denote the mean self-efficacy scores obtained from the "Control" group and *m*2 denote the mean self-efficacy scores obtained from the "Intervention" group.

If the research question is to determine whether the data provide significant evidence to conclude that women participating in the control group (no intervention) have less self- efficacy scores than women participating in the intervention on average, which one of the followings includes the appropriate null hypothesis and alternative hypothesis?

A. *H*0 :*m*1-*m*2 =0 versus *Ha *:*m*1-*m*2 10 B.*H*0:*m*1-*m*2=0versus *Ha*:*m*1-*m*2>0 C. *H*0 :*m*1-*m*2 =0 versus *Ha *:*m*1-*m*2 <0 D.*H*0:*m*1-*m*2£0versus *Ha*:*m*1-*m*2>0

PART C: Suppose that you are not certain whether the two populations of interest have the same standard deviations. Calculate the standard error of *x*1 - *x*2 (denoted by *SEx*1-*x*2 ).

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ONLINE STAT 2000 ONLINE MODULE 8 REVIEW LESSONS 1‐3

PART D: By hand, calculate the appropriate test statistic associated with the hypotheses

set up in PART B. What are the degrees of freedom for the test statistic? Use the

conservation approach (i.e. the smaller of *n *-1 and *n *-1 ) to determine the associated 12

degrees of freedom

PART E: Draw a sketch of a *t*-distribution curve and mark the location of your test statistic found in PART D. Shade the appropriate area that represents the *P-value*. Using an appropriate statistical table, approximate the P-value.

PART F: At the significance level of 0.001, do the data provide significant evidence to conclude that the population mean self-efficacy scores of women participating in the control group (no intervention) is less than the population mean self-efficacy scores of women participating in the intervention group? Justify your answer (i.e. How do you reach your conclusion?)

PROBLEM 2

The study of 584 longleaf pine trees in the Wade Tract in Thomas County, Georgia, had several purposes. Are trees in one part of the tract more or less like trees in any other part of the tract or are there differences? In this exercise we will examine the sizes of the trees, measured as diameter at breast height (DBH), by dividing the tract into eastern and western halves and taking random samples of 30 trees from each half. Here are the diameters in centimeters (cm) of the sampled trees:

The eastern distribution is right-skewed and the western distribution is left-skewed as shown in each histogram below.

30 25 20 15 10

5 0

Histogram

West

35

30

25

20

15

10

5 0

Histogram

East

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ONLINE STAT 2000 ONLINE MODULE 8 REVIEW LESSONS 1‐3

Below is the summary statistics for DBH each half of the tract:

PART A: Is it appropriate to use the methods of this section to compare the mean DBH of the trees in the east half of the tract with the mean DBH of trees in the west half? Give reasons for your answer.

A.The -methodsarenotappropriatebecausethetwodistributionsareskewed.

B.The -methodsarenotappropriatebecausethedistributionsofthenorthernand southern halves are not similar.

C.The -methodsareappropriatebecausethesamplesizesarerelativelylargeeven though the two distributions are skewed, and there are no outliers in either distribution.

D.The -methodsareappropriatebecausetheyarerobustagainstallkindsofdeviations from Normality.

PART B: Suppose that we use a *two-sided *significance test that help us investigate whether there is a significant evidence that the mean DBH of the trees in the eastern half of the tract is NOT the same as the mean DBH of the trees in the western half of the tract.

What is (are) the most appropriate reason(s) for your choice of using the two-sided test? Choose one correct answer.

A. The data shows us it is more likely that the western trees and the eastern trees have

different DBHs.

B. We have no reason to expect a difference in a particular direction.

C. The results from the two-sided test give more information.

D. A and B are correct.

E. A, B and C are correct.

PART C: Suppose that we use a *two-sided *significance test that help us investigate whether there is a significant evidence that the mean DBH of the trees in the eastern half of the tract is NOT the same as the mean DBH of the trees in the western half of the tract.

Let *m*1 denote the mean DBH of the trees in the west and *m*2 denote the mean DBH of the trees in the east.

State the appropriate null and alternative hypotheses in terms of *m*1 and *m*2 .

PART D: By hand, calculate the appropriate test statistic associated with the hypotheses

set up in PART C. What are the degrees of freedom for the test statistic? Use the

conservation approach (i.e. the smaller of *n *-1 and *n *-1 ) to determine the associated 12

degrees of freedom

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ONLINE STAT 2000 ONLINE MODULE 8 REVIEW LESSONS 1‐3

PART E: Draw a sketch of a t-distribution curve and mark the location of your test statistic found in PART D. Shade the appropriate area that represents the P-value. Using an appropriate statistical table, approximate the P-value.

PART F: Which one of the followings summarizes your conclusion based on the P-value found in PART D and the appropriate hypotheses stated in PART C?

A. At the 5% level of significance, we have significant evidence to suggest

DBH of the western trees is smaller than the mean DBH of the eastern trees.

B. At the 1% level of significance, we have significant evidence to suggest

DBHs of the two populations are different.

C. At the 5% level of significance, we have significant evidence to suggest

DBHs of the two populations are different.

MODULE 8: LESSON 2

PROBLEM 3

that the mean

that the mean

that the mean

An industrial psychologist is investigating the effects of work environment

attitudes. A group of 28 recently hired sales trainees were randomly assigned to one of 7 different "home rooms" - four trainees per room. Each room is identical except for wall color, with 7 different colors used. The psychologist wants to know whether room color has an effect on attitude, and, if so, wants to compare the mean attitudes of the trainees assigned to the 7 room colors. At the end of the training program, the attitude of each trainee was measured on a 100 -pt. scale (the lower the score, the poorer the attitude).

PART A: Identify the response variable in this study.

PART B: Identify the treatments for this study.

PART C: How many treatments are in this study ?

PART D: How many replications are in each treatment group ?

PART E: What is the total sample size in this study?

PROBLEM 4

In a completely randomized design experiment, 10 experimental units were randomly chosen for each of three treatment groups and a quantity was measured for each unit within each group. In the first steps of testing whether the means of the three groups are the same, the sum of squares for treatments was calculated to be 3,110 and the sum of squares for error was calculated to be 27,000.

PART A: Complete the ANOVA table. That is, find the values of a, b, c, d, e, f, g, h, and i.

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ONLINE STAT 2000 ONLINE MODULE 8 REVIEW LESSONS 1‐3

PART B: Which of the following is not a condition required for a valid One-Way ANOVA F- test for a completely randomized experiment?

A) The sampled populations all have distributions that are approximately normal. B) The samples are chosen from each population in an independent manner.

C) The variances of all the sampled populations are different.

PROBLEM 5

A partially completed ANOVA table for a completely randomized design is shown here.

PART A: Complete the ANOVA table.

PART B: How many treatments are involved in the experiment?

PART C: Do the data provide sufficient evidence to indicate a difference among the population means? Test using α = .05.

PROBLEM 6

An industrial psychologist is investigating the effects of work environment on employee attitudes. A group of 20 recently hired sales trainees were randomly assigned to one of four different "home rooms" five trainees per room. Each room is identical except for wall color. The four colors used were light green, light blue, gray, and red. The psychologist wants to know whether room color has an effect on attitude, and, if so, wants to compare the mean attitudes of the trainees assigned to the four room colors. At the end of the training program, the attitude of each trainee was measured on a 60-pt. scale (the lower the score, the poorer the attitude). The data was subjected to a one-way analysis of variance.

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ONLINE STAT 2000 ONLINE MODULE 8 REVIEW LESSONS 1‐3

PART A: Give the null hypothesis for the one-way ANOVA F-test shown on the computer output above.

- A) : where the ′ represent mean attitudes for the four rooms
- B) : where the ′ represent the proportion with the corresponding attitude
- C) : where the ′ represent attitude means for the person in each room
- D) : where the ′ represent the room colors

PART B: Using the one-way ANOVA table given above, identify the following values: Sum of Squares for Groups (SSG)=

Sum of Squares for Error (SSE)=

Degrees of Freedom in the numerator (DFG)=

Degrees of Freedom in the denominator(DFE)=

Mean Squares for Groups (MSG)=

Mean Squares for Error(MSE)=

PROBLEM 7

Four different leadership styles used by Big-Six accountants were investigated. As part of a designed study, 15 accountants were randomly selected from each of the four leadership style groups (a total of 60 accountants). Each accountant was asked to rate the degree to which their subordinates performed substandard field work on a 10 -point scale called the "substandard work scale". The objective is to compare the mean substandard work scales of the four leadership styles. The data on substandard work scales for all 60 observations were subjected to an analysis of variance.

ONE-WAY ANOVA FOR SUBSTAND BY STYLE SOURCE DF SS MS F P

BETWEEN WITHIN TOTAL

3 2728.17 909.390 5.210 0.003 56 9774.63 174.547

59 12,502.80

Interpret the results of the one-way ANOVA F-test shown on the printout for α = 0.05.

A) At α = .05, there is sufficient evidence of differences among the substandard work

scale means for the four leadership styles.

B) At α =.05, nothing can be said.

C) At α = .05, there is no evidence of interaction.

D) At α =.05, there is insufficient evidence of differences among the substandard work scale means for the four leadership styles

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ONLINE STAT 2000 ONLINE MODULE 8 REVIEW LESSONS 1‐3

PROBLEM 8

There have been numerous studies investigating the effects of restaurant ambience on consumer behavior. A recent study investigated the effects of musical genre on consumer spending. At a single high-end restaurant in England over a 3-week period, there were a total of 141 participants; 49 of them were subjected to background pop music (for example, Britney Spears, Culture Club, and Ricky Martin) while dining, 44 to background classical music (for example, Vivaldi, Handel, and Strauss), and 48 to no background music. For each participant, the total food bill, adjusted for time spent dining, was recorded. The following table summarizes the means and standard deviations:

PART A: State a set of hypotheses that is appropriate for investigating the effects of musical genre on consumer spending.

Let denote the followings:

*mC mP mN *

= the mean bill from the population subjected to background classical music.

= the mean bill from the population subjected to background pop music.

= the mean bill from the population subjected to no background music.

PART B: Is it reasonable to assume that the variances are equal in order to be pooled?

A. It is reasonable, because the sample variances are highly similar.

B. It is not reasonable, because the ratio of largest variance 11.10 to smallest variance 5.03 is greater than 2.

C. It is reasonable, because the ratio of largest standard deviation . 0.481 to . √

smallest standard deviation √ 0.338 is less than 2.

D. It is reasonable, because the ratio . 1.49 is less than 2.

.

PART C: Give the numerator degrees of freedom and the denominator degrees of

freedom associated with the F-statistic for the hypotheses set up in PART A.

PART D: A computer software computed the sum of squares for groups of 164.66 and the sum of squares for error of 1,069.39. Calculate the *F *statistic for the hypotheses set up in PART A.

PART E: Given that a computer software gives the P-value of 0.00005, which of the following is the most appropriate conclusion?

A. We have strong evidence that the means are all the same.

B. We have strong evidence that the means are not all the same.

C. We have strong evidence that the mean is higher for classical music.

D. We have strong evidence that the mean for classical music is different from the other

two means.

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MODULE 8: LESSON 3

PROBLEM 9

A study of 865 college students found that 42.5% had student loans. A single random sample of 865 college students were randomly selected from the approximately 30,000 undergraduates enrolled in a large public university. The overall purpose of the study was to examine the effects of student loan burdens on the choice of a career. A student with a large debt may be more likely to choose a field where starting salaries are high so that the loan can more easily be repaid. The following table classifies the students by field of study and whether or not they have a loan:

PART A: Identify the explanatory variable and the response variable in this study.

PART B: Suppose that we are investigating to determine whether there is significant evidence that "Student loan" and "Field of study" are dependent. State an appropriate set of hypotheses.

PART C: If it is true that "Student loan" and "Field of study" are independent, how many students who study Science and who have student loans would you expect to see from the sample?

PART D: The partial Excel output using MegaStat add-in for the above table is given below. The output includes the observed cell counts (in yellow), the expected cell counts (in green), and the contributions to the chi-square statistic in orange cells. Some expected cell counts and some contributions to are missing.

Recall that a contribution to is calculated by which is

represented by in the MegaStat output below.

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ONLINE STAT 2000 ONLINE MODULE 8 REVIEW LESSONS 1‐3

Answer the following questions below:

(1)What is the expected cell count for students who study Science and who have student

loans?

(2)What is the expected cell count for students who study Agriculture and who do not

have student loans?

(3)Is the chi-square test appropriate for performing the significance test of the

hypotheses in PART A? Why or why not?

- (4) What is the value of ?

- (5)How many values of the response variable are there?That is, how many rows

(excluding the total row) are there in the two-way table (given above PART A)?

(6)How many values of the explanatory variable are there?That is, how many columns

(excluding the total column) are there in the two-way table (given above PART A)?

(7) What is the degrees of freedom for the chi-square statistic ?

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PART E:

The area (in read on the right) on the

right tail of the chi-square distribution with the degrees of freedom found in PART D represents the P-value associated with the chi-square statistic . Using Table F

, approximate the P-value.

PART F: Using the significance level of 0.05, what do the results of the significance test show? Choose one correct answer.

A. There is no significant evidence that having a loan and field of study are related.

B. There is significant evidence that having a loan and field of study are related.

C. There is significant evidence that having a loan and field of study are not related.

PROBLEM 10

Because statistical software plays such an important role in modern statistical applications, many studies have encouraged the use of technology in statistics courses. The Guidelines for the Assessment and Instruction in Statistics Education (GAISE) (Aliaga et al., 2005) project was funded by the American Statistical Association to examine needs for college level statistics courses. One of the six recommendations from GAISE is the use of technology for developing conceptual understanding and analyzing data. Suppose a survey was sent to 115 students at different universities across the United States to access the relationship between ease of learning the statistical software program SAS and a student's currently level of SAS proficiency. The results of the survey are are shown below.

To access the relationship between ease of learning the statistical software program SAS

and a student's currently level of SAS proficiency, the appropriate hypotheses are

: of learning the statistical software program SAS and a student′s currently level of SAS are independent. : of learning the statistical software program SAS and a student′s currently level of SAS are dependent.

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PART A: If the null hypothesis is true, how many students who find SAS to be somewhat easy to learn and who are somewhat proficient in SAS would you expect to see in the sample?

PART B: The partial Excel output using MegaStat add-in for the above table is given below. The output includes the observed cell counts (in yellow), the expected cell counts (in green), and the contributions to the chi-square statistic in orange cells. Some expected cell counts and some contributions to are missing.

Recall that a contribution to is calculated by which is

represented by in the MegaStat output below.

Answer the following questions below:

(1) What is the contribution to for students who find SAS to be somewhat easy to learn and who are somewhat proficient?

- (2) Which cell contributes most to the chi-square statistic ?
- (3) What is the value of the chi-square statistic ?

PART C: Determine if the following statement is appropriate. Give your reasons.

At 1% level of significance, there is sufficient evidence to suggest that ease of learning the statistical software program SAS and a student's currently level of SAS proficiency are dependent.

PROBLEM 11

Following complaints about the working conditions in some apparel factories both in the United States and abroad, a joint government and industry commission recommended in 1998 that companies that monitor and enforce proper standards be allowed to display a "No Sweat" label on their products. Does the presence of these labels influence consumer behavior? A survey of U.S. residents aged 18 or older asked a series of questions about how likely they would be to purchase a garment under various conditions. For some conditions, it was stated that the garment had a "No Sweat" label; for others, there was no mention of such a label. On the basis of the responses, each person was classified as a "label user" or a "label nonuser." There were 296 women surveyed. Of these, 63 were label users. On the other hand, 27 of 251 men were classified as users.

PART A: Display the data in a two-way table. Use the columns for the values of the

explanatory variable in the study and the rows for the values of the response variable in the study.

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PART B

Suppose we want to perform an appropriate significant test to determine whether or not there is a relationship between gender and use of No Sweat labels.

Give an appropriate set of hypotheses, an appropriate test statistic, its associated degrees of freedom, and its associated P-value. Use TABLE F to approximate the P-value.

PART C

Using the significance level of 0.0025, which of the followings is the appropriate conclusion?

A. There is no significant evidence that gender and label use are dependent.

B. There is significant evidence that gender and label use are dependent.

C. There is significant evidence that gender and label use are independent.