# Project #122491 - Statistics Quantitative Research

1. The Chicago Tribune of July 21, 1995 reported on a study by a fourth-grade student named Beth Peres. In the process of collecting evidence in support of her campaign for a higher allowance, she polled her classmates on what they received as an allowance. She was surprised to discover that the 11 girls who responded reported an average allowance of \$2.63 per week, while the 7 boys reported an average of \$3.18, 21% more than for the girls. At the same time boys had to do fewer chores to earn their allowance than did girls. The story had a considerable national prominence and raised the question of whether the income disparity for adult women relative to adult men may actually have its start very early in life.
1. (2 points) What are the dependent and independent variables in this study? How are they measured?
2. (2 points) What kind of a sampling method are we dealing with here?
3. (2 points) How could the characteristics of the sample influence the results she obtained?
4. (2 points) How might Beth go about “random sampling?” How would she go about “random assignment?”
5. (2 points) If random assignment is not possible in this study, does that have negative implications for the validity of the study?
6. (2 points) What are some of the variables that might influence the outcome of this study separate from any true population differences between boys’ and girls’ income?
7. (2 points) Distinguish clearly between the descriptive and inferential statistical features of this example.

1. (3 points) We have sent out everyone in a large introductory course to check whether people use seat belts. Each student has been told to look at 100 cars and count the number of people wearing seat belts. The number found by any given student is considered that student’s score. The mean score for the class is 44, with a standard deviation of 7. Assume that the counts are normally distributed. A student who has done very little work all year has reported fining 62 seat belt users out of 100. Do we have reason to suspect that the student just made up a number rather than actually counting? (Hint: Calculate the standard score, z, of this raw score, z = (X – M)/SD = (62 - 44) / 7 = 2.57, and interpret what the z score means.)

1. (3 points) A researcher analyzed the results of an experiment and found that the obtained t-value (on a t-test of independent means) was 1.29, with a total of 25 children in group 1 and 30 children in group 2. Use the table of critical values and discuss whether the null hypothesis can or cannot be rejected.

1. (3 points) Peter, a sixth-grade mathematics teacher, recently administered an exam.  He wants to report a measure of central tendency but he doesn’t know what to do with the fact that two students have much lower scores than anyone else.  What is the best measure of central tendency for Peter to report?

a.    Range

b.    Standard deviation

c.    Median

d.   Mean

1. (3 points) Maricella has collected her thesis data that examines differences in PSAT math achievement in Latino boys and girls.  However, upon a second look at the graphs of her raw scores, it appears that the boys’ scores are more normally distributed and the girls’ scores are somewhat more bunched together around the mean.  Given this information, what can you conclude regarding the data set?

a.        The standard deviation is likely smaller for girls.

b.       The girls’ distribution is likely unimodal.

c.        The girls’ mean score is more representative of the data.

d.       The girls’ median is higher than the boys’ median.

Use the following scenario for Q. 6 and Q. 7:

Anton collected survey data regarding teachers’ use of technology in their teaching activities. He was pleased that his data are generally normally distributed.  Among other data, he collected age, number of years teaching, highest degree held, amount of time spent in online office hours weekly, and whether the teacher reported using an electronic discussion board.

1. (3 points) Anton will most likely report which of the following measures of central tendency for the variable number of years teaching?

a.        Mode

b.       Range

c.        Mean

d.       Median

1. (3 points) Anton will most likely report which of the following measures of central tendency for the variable highest degree held?

a.          Mode

b.         Range

c.          Mean

d.         Median

1. (3 points) Andy compared students’ ability to transfer learning from three different types of instructional materials.  He found that there were pre-existing group differences between his conditions.  Which of the following is the appropriate analysis technique for Andy to use?

a.  Nonindependent t-test

b.  Independent t-test

c.  MANOVA

d. ANCOVA

1. (3 points) Nelson’s recent study tested differences in problem-solving ability based upon science ability, treatment (instruction, no instruction), and gender.  Of the following, which test should Nelson employ?

a.  Chi Square

b.  t-test

c.  ANOVA

d. Multiple Regression

1. Foa, Rothbaum, Riggs, and Murdock (1991) conducted a study evaluating four different types of therapy for rape victims. The Stress Inoculation Therapy (SIT) group received instructions on coping with stress. The Prolonged Exposure (PE) group went over the events in their minds repeatedly. The Supportive Counseling (SC) group were taught a general problem-solving technique. Finally, the Waiting List (WL) control group received no therapy. Data with the same characteristics as theirs follow, where the dependent variable was the severity rating of a series of symptoms.

 Group n Mean S.D. SIT 14 11.07 3.95 PE 10 15.40 11.12 SC 11 18.09 7.13 WL 10 19.50 7.11

1. (3 points) The analysis of variance (ANOVA) was run, and the results are in the following table. Draw whatever conclusions are warranted. Interpret what the conclusions mean.

 Source df SS MS F Treatment 3 507.840 169.280 3.04* Error 41 2279.067 55.587 Total 44 2786.907 * p < .05

1. (3 points) The Bonferroni test was run to compare the WL group with each of the other three groups. The results are in the following table. What would you conclude? How does this compare to the answer to part a?

 WL versus SIT WL versus PE WL versus SC t = 2.73 t = 1.23 t = 0.433

The critical value of the Bonferroni test is 2.50.

For Q. 11 and Q. 12: Chloe concluded that there were differences in achievement goals between those who had completed a ropes course and those who did not complete the course.  However, there were no true differences between groups.  The ropes course had no significant effect on achievement goals.

11.  (3 points) In this scenario, Chloe’s conclusion represents a

a.       Type I error.

b.      Type II error.

c.       Type III error.

d.      Type IV error.

12.  (3 points) To determine if there were significant differences between groups, Chloe would have conducted which of the following analyses?

a.      Chi Square

b.      Pearson r

c.      t-test

d.     ANOVA

For Q. 13 through Q. 16: In her study of student athletes’ achievement motivation, Katie administers a self-report achievement motivation scale before she starts a new motivation enhancement intervention.  After the intervention, Katie again assesses students’ achievement motivation. She set her alpha at p=.05, and reports that there were no significant findings in her study.

13.  (3 points) Which of the following best represents the design of Katie’s study?

a.         Experimental

b.         Cross-sectional

c.         Correlational

d.        Pre-experimental

14.  (3 points) Which statistical analysis was appropriate for Katie to use to determine if there were treatment differences in her study?

a.         Pearson r

b.         ANOVA

c.         Spearman rho

d.        t-test

15.  (3 points) Katie questions whether there are significant differences in her study but her significance level is unable to detect these differences. What type of error is Katie most concerned that she is committing?

a.        Type I

b.       Type II

c.        Type III

d.       Type IV

16.  (3 points) From the following options, how would you advise Katie regarding her analyses?

a.        Change your probability level to p=.001.

b.       Evaluate and conduct the study with a new sample.

c.        Reanalyze with a two-tailed analyses.

d.       Use a nonparametric significance test.

1. (8 points) Identify the problem with each of the following questionnaire items:

a.       Which is the most serious social problem in the U.S. today, anomie or oversocialization?

b.      Do you think there is a good market for the product and that it will sell well?

c.       Don’t you think that in these days of escalating costs of living, employees should be given good pay raises?

d.      A set of response categories to the question “What is your current age?” is:

i.      1-5

ii.      5-10

iii.      10-20

iv.      20-30

v.      30-40

1. (6 points) Below are listed the steps in the process of testing a hypothesis in a quantitative study. Place the steps in order from 1 to 6 with 1 as the first step and 6 as the last step.

_________ Compute the sample statistic

_________ Establish the null hypothesis

_________ Collect data

_________ Make a decision about rejecting or failing to reject the null

_________ Set the level of significance (alpha)

_________ Determine the practical significance of the results

1. (3 points) Julia stands on a pair of scales three times in a row. The first time she weighs 69 kilo, the second time 69 kilo, and the third time 69 kilo. Her real weight is 51 kilo. What is the matter with the scales?

a.       The pair of scales is not reliable and not valid.

b.      The pair of scales is reliable but is not valid.

c.       The pair of scales is not reliable but is valid.

d.      The pair of scales is reliable and valid.

20.  (8 points) What kinds of sampling designs would be used for each of the following?

a.       A study to get a quick idea of the medical acceptability of a new aspirin substitute which cannot be dispensed over the counter without prescription.

b.      A study involving a sample of 325 students in a university where 2,000 students are enrolled.

c.       An investigation of the career salience of professionals in the fields of medicine, engineering, business, and law.

d.      The generalizability of the attitudes of blue collar workers from a sample of 184, to the total population of 350 blue collar workers in the entire factory of a particular company.

1. (5 points) Examine the following results reported in a quantitative study:

“The scores varied for band members (M=3.5), choir members (M=3.9), and for student athletes (M=5.4) for attitudes toward engaging in school activities during the 3-5 p.m. period of time. A comparison of the groups, at an alpha of .05, showed a statistically significant difference among the three groups, F (3, 8) = 9.87, p = .031, effect size = .91 SD.”

As you examine this statement, you conclude: (place an X in the appropriate column)

 NO YES The null hypothesis was rejected. The level of significance showed a probability of rejecting set at 5 out of 100 times. The statistical test used was a t-test. The magnitude of differences among the groups was over one standard deviation. Band members differed significantly from student athletes in their attitudes.

22.  (8 points) Below is a tabulation of the demographic data from the Frequency distribution of a survey done by Ms. Sandra Jones. Her sample consisted of 148 of a total of 3,700 clerical employees in three service organizations.

Part I (2 points): Based on the tabulation provided below, describe the sample characteristics.

Table 1: Frequency Distributions of Sample (n = 148)

 Race Education Gender Non-whites = 48 (32%) High School = 38 (26%) Males    = 111(75%) Whites        = 100 (68%) College Degree = 74 (50%) Females = 37 (25%) Masters Degree = 36 (24%)

 Age # of Years in Org. Marital Status < 20    = 10(7%) < 1 year = 5 (3%) Single 20 (14%) 20-30 = 20(14%) 1-3         = 25(17%) Married 108 (73%) 31-40 = 30(20%) 4-10       = 98(66%) Divorced 13 (9%) >40   = 88(59%) >10       = 20(14%) Alternative Lifestyle 7 (4%)

Part II (3 points): Here is another tabulation of the Means, Standard Deviations, etc., for Ms. Jones’ data. How would you interpret these data?

Table 2: Means, Standard Deviations and Other Statistics

 VARIABLE MEAN STD. DEV MODE MIN MAX Age 37.5 18 38 20 64 # of Years Married 12.1 24 15 0 32 Stress 3.7 1.79 3 1 5 Job Involvement 3.9 1.63 4 2 5 Performance 3.6 0.86 3 3 5

Part III (3 points): From the same research done by Ms. Jones, the following inter-correlation matrix is shown. Interpret these results.

Table 3: Pearson Correlations

 Variable Age # of yrs. Married Stress Job Involvement Performance Age 1.0 # of yrs. married .86 1.0 Stress -.43 -.61 1.0 Job Involvement .53 .32 .58 1.0 Performance .09 -.06 .49 .36 1.0

a. All correlations above .30 are significant, at least at the .05 level.

b. All correlations above .50 are significant, at least at the .01 level.

 Subject Mathematics Due By (Pacific Time) 04/27/2016 12:00 am
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