Question

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?

Answer 1

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

H₀: µ_d = 0 versus H_a: µ_d ≠ 0

Question 2

From given data, we have

Dbar = 54.1000

S_d = 58.4854

n = 10

df = n – 1 = 9

α = 0.05

Critical value = -/+ 2.2622

(by using t-table)

Test statistic = t = (Dbar - µ_d) / [ S_d/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*S_D/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