Question

In: Statistics and Probability

a researcher at the univeristy of vermont was interested in studying the relationship between attorneys' decision...

a researcher at the univeristy of vermont was interested in studying the relationship between attorneys' decision to prosecute cases and victims' credibility. she collected data on 4205 cases, her two variables were victims' credibility(coded as 0=low, 1=medium, 2=high) and case prosecuted(coded as 0=no, 1=yes). Of the 2713 cases prosecutes , in 1025 cases the victim had high credibility, in 790 of the cases the victim had medium credibility and in 989 cases the victim had low credibility . Of the 1492 cases that were not prosecuted, in 541 the victim had high credibility, in 745 the victim had medium credibility, and in 206 the victim had low credibility.

Victims credibility

Cases Prosecuted low med high

no 206 745 541

yes 898 790 1025

a. What are the independent and dependent variable?

b. Is there a statistically significant relationship bewteen victim's credibility and the prosecutors decision to prosecute? (Be sure to write out the six steps)

c. What type of error might you be making ? and how could you reduce the likelihood of making that type or error?

d. What percentage of cases were prosecuted in this sample?

e. For those cases where the victims had high credibility, what percentage were prosecuted?

Solutions

Expert Solution

a:

Independent variable: Cases prosecuted

Dependent variable: Victims credibility

b:

Here we need to use hi square test of independence.

Hypotheses are:

H0: There is no statistically significant relationship between victim's credibility and the prosecutors decision to prosecute.

Ha: There is a statistically significant relationship between victim's credibility and the prosecutors decision to prosecute.

Let level of significance:

Degree of freedom: df =( number of rows -1)*(number of columns-1) = (2-1)*(3-1)=2

The critical value using excel function "=CHIINV(0.05,2)" is 5.991

Rejection region:

If , reject H0

Following table shows the row total and column total:

Victims credibility
Low Med High Total
Cases Prosecuted No 206 745 541 1492
Yes 898 790 1025 2713
Total 1104 1535 1566 4205

Expected frequencies will be calculated as follows:

Following table shows the expected frequencies:

Victims credibility
Low Med High Total
Cases Prosecuted No 391.717 544.642 555.641 1492
Yes 712.283 990.358 1010.359 2713
Total 1104 1535 1566 4205

Following table shows the calculations for chi square test statistics:

O E (O-E)^2/E
206 391.717 88.05031206
898 712.283 48.42289383
745 544.642 73.70589885
790 990.358 40.53415852
541 555.641 0.385786652
1025 1010.359 0.212161104
Total 4205 4205 251.311211

Following is the test statistics:

Conclusion:

Since test statistics lies in rejection region so we reject the null hypothesis.

That is we can conclude that there is a statistically significant relationship between victim's credibility and the prosecutors decision to prosecute.

c)

Since we reject the null hypothesis so type I error is possible. To reduce the likelihood of making that type I we need to reduce the level of significance.

d)

The percentage of cases were prosecuted in this sample is

(2713 /4205 ) *100% = 64.52%

e)

The required percentage is

(1025 / 1566) *100% = 65.45%


Related Solutions

A researcher is interested to learn if there is a relationship between the level of interaction...
A researcher is interested to learn if there is a relationship between the level of interaction a women in her 20s has with her mother and her life satisfaction ranking. Below is a list of women who fit into each of four level of interaction. Conduct a One-Way ANOVA on the data to determine if a relationship exists. State whether or not a relationship exists and why or why not. Explain in as much detail as possible. No Interaction Low...
A researcher is interested to learn if there is a linear relationship between the hours in...
A researcher is interested to learn if there is a linear relationship between the hours in a week spent exercising and a persons life satisfaction. The researchers collected the following data from a random sample, which included the number of hours spent exercising in a week and a ranking of life satisfaction from 1 to 10 ( 1 being the lowest and 10 the highest). Participant Hours of Exercise Life Satisfaction 1 3 1 2 14 2 3 14 4...
A sports researcher is interested in determining if there is a relationship between the number of...
A sports researcher is interested in determining if there is a relationship between the number of home wins depends on the sport. A random sample of 200 games is selected and the results are given below. Football Basketball Soccer Baseball Home team wins 30 20 15 35 Visiting team wins 20 30 35 15 What is the test statistic value for the above data? A 4 B 10 C 20 D None of the above
A sports researcher is interested in determining if there is a relationship between the number of...
A sports researcher is interested in determining if there is a relationship between the number of home team and visiting team wins and different sports. A random sample of 633 games is selected and the results are given below. Conduct test of hypothesis to test the claim that the number of home team and visiting team wins is independent of the sport. Use a=0.05. Football BasketBall Soccer Baseball Hometeam Wins 89 165 91 49 Visiting Team Wins 60 89 52...
A researcher is interested to learn if there is a linear relationship between the hours in...
A researcher is interested to learn if there is a linear relationship between the hours in a week spent exercising and a person’s life satisfaction. The researchers collected the following data from a random sample, which included the number of hours spent exercising in a week and a ranking of life satisfaction from 1 to 10 ( 1 being the lowest and 10 the highest). PLEASE help in SPSS. Participant Hours of Exercise Life Satisfaction 1 3 1 2 14...
A researcher believes that there is a positive relationship between the time spent in studying and...
A researcher believes that there is a positive relationship between the time spent in studying and the score a student gets at the end of the semester. She selected a sample of students and recorded the following data: Time Spent in minutes Score out of 100 120 86 75 83 60 78 45 75 180 91 30 72 90 84 After analyzing the data using Microsoft Excel, the researcher got the outputs below: Answer the following (Please, use at least...
A teacher is interested in the relationship between the time spent studying for an exam and...
A teacher is interested in the relationship between the time spent studying for an exam and exam score. The table lists scores for 5 students. The value of b0 = 67.91 and the value of b1 = 0.75 Hours studied 5 18 3 15 17 Exam score 63 87 79 72 82 . Step 4 of 6 : Calculate the Coefficient of Determination (R2). Round answer to four decimal places.
A researcher is interested in determining whether there is a relationship between the weekly number of...
A researcher is interested in determining whether there is a relationship between the weekly number of room air-conditioning units sold and the time of year. What type of descriptive chart would be most useful in performing this analysis? Explain your choice.
A researcher is interested in a possible relationship between height and the time it takes to...
A researcher is interested in a possible relationship between height and the time it takes to run a 100 meters. With a random sample of 57 people, the researcher finds a Pearson correlation coefficient r = − 0.492. Group of answer choices A. There is a very strong correlation between these variables. As height increases, generally the 100-meter run time decreases. B. There is a very strong correlation between these variables. As height increases, generally the 100-meter run time increases...
***SHOW SPSS** A researcher is interested to learn if there is a linear relationship between the...
***SHOW SPSS** A researcher is interested to learn if there is a linear relationship between the hours in a week spent exercising and a person’s life satisfaction. The researchers collected the following data from a random sample, which included the number of hours spent exercising in a week and a ranking of life satisfaction from 1 to 10 ( 1 being the lowest and 10 the highest). Participant Hours of Exercise Life Satisfaction 1 3 1 2 14 2 3...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT