Question

In: Statistics and Probability

A group of I-O psychologists were interested in whether listening to the radio or an audio...

A group of I-O psychologists were interested in whether listening to the radio or an audio book while working would result in greater productivity of factory workers (defined by pounds of product produced). Therefore, the researchers visited a factory in Pennsylvania that has 10-full-time employees. They first recorded the pounds of product produced by each employee while listening to a local music radio station on Wednesday of week 1. Then on Wednesday of week 2, the researchers recorded the pounds of product produced by each employee while listening to an audio book. The data is as follows:

Employee

Pounds During Music

Pounds During Audio Book

1

1095

947

2

988

974

3

1044

1032

4

1081

922

5

1016

1005

6

1026

974

7

1058

1016

8

1045

958

9

1018

999

10

982

985

With the above data, answer the following:

1. State the appropriate alternative and null hypotheses (using the statistical notation for stating mathematical relationships) to test the hypothesis that the pounds of product produced by the employees while listening to music is different than when listening to an audio book.

2. Assuming an alpha level of 0.05, provide the critical and obtained values for this hypothesis test.

3. Assuming an alpha level of 0.05, make a decision as to whether the result of the hypothesis test is significant or insignificant, as well as whether you should reject or fail to reject the null hypothesis, being sure to explain why. Also, interpret the results of the hypothesis test in everyday language (i.e., does productivity differ depending on whether the employees are listening to music or an audio book?).

4. What are the upper and lower boundaries of the range of population mean differences that you can say with 95% confidence contains the mean difference represented by the above sample?

Solutions

Expert Solution

Question 1

Null hypothesis: H0: The pounds of product produced by the employees while listening to music are same as when listening to an audio book.

Alternative hypothesis: Ha: The pounds of product produced by the employees while listening to music is different than when listening to an audio book.

H0: µd = 0 versus Ha: µd ≠ 0

Question 2

From given data, we have

Dbar = 54.1000

Sd = 58.4854

n = 10

df = n – 1 = 9

α = 0.05

Critical value = -/+ 2.2622

(by using t-table)

Test statistic = t = (Dbar - µd) / [ Sd/sqrt(n)]

t = (54.1000 – 0) / [58.4854/sqrt(10)]

t = 2.9252

P-value = 0.0169

(by using t-table)

Question 3

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the pound of product produced by the employees while listening to music is different than when listening to an audio book.

Question 4

Confidence interval = Dbar ± t*SD/sqrt(n)

Confidence interval = 54.1000 ± 2.2622*58.4854/sqrt(10)

Confidence interval = 54.1000 ± 41.83872705

Lower limit = 54.1000 - 41.83872705 =12.26127

Upper limit = 54.1000 + 41.83872705 = 95.93873


Related Solutions

I was listening to my radio one night and I noticed that when I turned on...
I was listening to my radio one night and I noticed that when I turned on my desk light there was a little blip of noise on the radio. I repeated this and I noticed that when I was on the border of completing the circuit, such that when the bulb was flickering, I got severe interference on my radio. My radio was running on batteries. Why does this happen?
Who are three I/O theorists or psychologists and describe the potential impact of their research methods
Who are three I/O theorists or psychologists and describe the potential impact of their research methods
A group of psychologists is investigating whether exposure to outside spaces influences altruism. They gather a...
A group of psychologists is investigating whether exposure to outside spaces influences altruism. They gather a group of subjects and ask them to take a test, during the test, they are asked how much they would donate to a charity. Half of the subjects take the test in a windowless room, the other half take the test in the university’s garden. The researchers believe the subjects in the garden will donate more on average. Which of the following best describes...
Question #5: Educational psychologists were interested in the impact the "Just Say No!" Program and contracts...
Question #5: Educational psychologists were interested in the impact the "Just Say No!" Program and contracts on drunk driving among males vs. female teenagers. With the cooperation of school officials, 16-year-old students were matched and randomly assigned to one of two groups, with equal numbers of males and females in each group. Group A participated in a "Just Say No!" program, which required a one-hour information session instead of P.E. for six weeks. Students were presented with written factual information,...
A group of psychologists want to examine whether different types of psychotherapy work better for adolescent...
A group of psychologists want to examine whether different types of psychotherapy work better for adolescent depression. One group of n1 = 4 adolescents were given Cognitive-Behavioral therapy, a second group of n2 = 4 adolescents were given Psychodynamic therapy, and a third group of n3 = 4 adolescents were placed on a Waitlist Control condition. At the end of 10-weeks, each participant comnpletes a depression screening (higher scores mean more depressed). The data are below. Psychotherapy Type Cognitive-Behavioral Psychodynamic...
Q1. Researchers were interested in determining whether there were any differences in the tendency to procrastinate...
Q1. Researchers were interested in determining whether there were any differences in the tendency to procrastinate based on birth order, i.e. first, second, or third child born. Using the data in the table below, answer the following questions. State the null and alternate hypotheses. What is the total sample size? Identify the independent and dependent variables What is the test statistic value? What is the p value? What is your conclusion (assume α = .05)? Phrase your conclusion based on...
Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the...
Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the same average age across the country. Suppose that the following data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which teenagers obtained their drivers licenses. Use a level of significance of 0.10. Northeast      South           West            Central 16.3              16.9              16.4              16.2    16.1              16.5              16.5              16.6    16.4              16.4              23.0              16.5    16.5              16.2              20.2              16.4    What...
Investigators are interested in whether a new diet lowers total cholesterol in a group of individuals....
Investigators are interested in whether a new diet lowers total cholesterol in a group of individuals. They take a sample of 28 participants on the new diet. They know that the mean cholesterol level of the general population (µ) is 201 mg/dL, but they do not have information on the standard deviation of the population. The mean total cholesterol level in their sample of participants is 195 mg/dL and their sample has a standard deviation of 9 mg/dL. Your research...
Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the...
Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the same average age across the country. Suppose that the following data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which teenagers obtained their drivers licenses. Use a level of significance of 0.10. Northeast      South           West            Central 16.3              16.9              16.4              16.2     16.1              16.5              16.5              16.6     16.4              16.4              23.0              16.5     16.5              16.2              20.2              16.4    What...
Researchers were interested in determining whether there was a difference in crime rates in areas where...
Researchers were interested in determining whether there was a difference in crime rates in areas where there is high youth unemployment vs low youth unemployment. Alpha (level of significance) was set at .05. State the null and alternate hypotheses. What is the independent variable? What is the dependent variable? Complete the table below: Low Youth Unemployment High Youth Unemployment Sample Size Sample Mean Sample Standard Deviation Estimated Standard Error Group Statistics High Youth Unemployment N Mean Std. Deviation Crime rate...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT