Question

1. At the emergency room at the one hospital, the nurses are convinced that the number of patients that they see during the midnight shift is affected by the phases of the moon. The doctors think this is an old wives’ tale. The nurses decided to test their theory at the 0.10 level of significance level by recording the number of patients they see during the midnight shift for each moon phase over the course of one lunar cycle. The results are in the table below.  ( can do by hand or using JMP)

ER patients During the Midnight Shift
	New Moon	1st Quarter	Full Moon	3 rd Quarter
Number of patients	85	66	97	68

1. State the null and alternative hypotheses testing the nurses claim.
2. Compute the expected count  for “New Moon” cell
3. Compute Chi-square for “ New Moon” cell
4. Assuming assumptions are satisfied, state a decision, draw a conclusion and interpret your conclusion.

2. A local fast-food restaurant serves buffalo wings. The restaurant’s managers notice that they normally sell the following proportions of flavors for their wings: 20% Spicy Garlic, 50% Classic Medium,10% Teriyaki, 10% Hot BBQ and 10% Asian Zing. After running a campaign to promote their nontraditional specialty wings, they want to know of the campaign has made an impact. The results after 10 days are listed in the following table. ( By hand or using JMP)

Buffalo Spicy Wings
	Number Sold
Spicy Garlic	251
Classic Medium	630
Teriyaki	115
Hot BBQ	141
Asian ZIng	121

1. State the Null and Alternative hypotheses
2. Check the appropriate assumptions for this test.
3. Is there sufficient evidence at 0.05 significance level to conclude that the promotional campaign has made any difference in the proportions of flavors sold? Interpret your conclusion

3. According to an online survey b Harris Interactive for job site CareerBuilder.com more than half of IT workers say they have fallen asleep at work. The same is also true for government workers. Assume the following contingency table is representative of the survey results.

	Job  Category
Slept of the Job?	IT professional	Government Professional
Yes	155	256
No	145	144

1. Which test will use with that example (circle):    

Chi-square Goodness-of Fit       Chi-square of Independence

2. State the Null and Alternative Hypotheses:

H₀:

H_A:

3. Create an appropriate graph to summarize these data. (use JMP)
4. At 0.05 significance level, can we conclude that sleeping on the job depends on job category?
5. If you rejected the Null hypothesis in part d), compute a 95%CI. Interpret this 95% whether there is a difference between the proportion of IT and Government  workers who have fallen asleep at work.

Thank you! I'll like your answer!

Answer 1

1)

a)

Ho: two varaibles are as expected
H1:two variables are not as expected

b)

observed frequencey, O	expected proportion	expected frequency,E			(O-E)²/E
85	0.250	79.00			0.456
66	0.250	79.00			2.139
97	0.250	79.00			4.101
68	0.250	79.00			1.532

c)

chi square test statistic,X² = Σ(O-E)²/E =   8.228              
                  
level of significance, α=   0.1              
Degree of freedom=k-1=   4   -   1   =   3
                  
P value =   0.0415   [ excel function: =chisq.dist.rt(test-stat,df) ]          
Decision: P value < α, Reject Ho          

Conclusion: New moon effects the results.

---------------------------

2)

observed frequencey, O	expected proportion	expected frequency,E			(O-E)²/E
251	0.200	251.60			0.001
630	0.500	629.00			0.002
115	0.100	125.80			0.927
141	0.100	125.80			1.837
121	0.100	125.80			0.183

chi square test statistic,X² = Σ(O-E)²/E =   2.950              
                  
level of significance, α=   0.05              
Degree of freedom=k-1=   5   -   1   =   4
                  
P value =   0.5662   [ excel function: =chisq.dist.rt(test-stat,df) ]          
Decision: P value >α , Do not reject Ho                  

Conclusion: We can conclude that the promotional campaign has not made any difference in the proportions of flavors sold

Thanks in advance!

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