Question

a. Please state both the null and alternative hypotheses for this question. b. Provide the decision rule for making this decision. Use an alpha level of .05. c. Show all the work necessary to calculate the appropriate statistic. d. What conclusion are you allowed to draw? Write a conclusions sentence in APA format (i.e., it includes the appropriate statistical information).

A researcher is interested in whether a significant trend exists regarding the popularity of certain work shifts among police officers. A random sample of 60 police officers is selected from a large metropolitan police force. The officers are asked to indicate which of three work shifts they preferred. The results show that 40 officers prefer the first shift, 10 prefer the second shirt, and 10 prefer the third shift. Do the results deviate significantly from what would be expected due to chance?

Answer 1

(a)

H0: Null Hypothesis: The results do not deviate significantly from what would be expected due to chance.

HA: Alternative Hypothesis: The results deviate significantly from what would be expected due to chance.

(b)

= 0.05

ndf = n - 1 =3 - 1= 2

From Table, critical values of = 5.9915

Decision Rule:

Reject H0 if > 5.9915

(c)

Assuming H0, the Expected Frequency of each shift = 60/3 = 20

Test Statistic is calculated as follows:

Shift	Observed Frequency (O)	Expected Frequency (E)	(O - E)2/E
First Shift	40	20	20.00
Second Shift	10	20	5.00
Third Shift	10	20	5.00
Total = =			30.00

So,

Test Statistic = 30.00

(d) Since calculated value of = 30.00 is greater than critical value of , the difference is significant. Reject null Hypothesis.

(e) Conclusion:
The data support the claim that the results deviate significantly from what would be expected due to chance. A significant trend exists regarding the popularity of certain work shifts among police officers.