Question

A hospital wants to determine if the type of treatment for pneumonia is a factor in recovery time? The table below shows the number of days to recovery for several randomly selected pneumonia patients that had various types of treatment.

Sent Home With Medicine	A Few Hours in the Hospital	Overnight Hospital Stay
22	8	8
19	15	18
18	12	18
22	23	4
27	18	5
14	10	10
30	18	18
23	8	8
	9	17

Assume that all distributions are normal, the three population standard deviations are all the same, and the data was collected independently and randomly. Use a level of significance of α=0.1α=0.1.

H0: μ1=μ2=μ3H0: μ1=μ2=μ3
H1:H1: At least two of the means differ from each other.

1. For this study, we should use Select an answer 1-PropZInt χ²GOF-Test 1-PropZTest 2-PropZTest χ²-Test 2-SampTTest T-Test ANOVA TInterval 2-SampTInt 2-PropZInt
2. The test-statistic for this data =  (Please show your answer to 3 decimal places.)
3. The p-value for this sample =  (Please show your answer to 4 decimal places.)
4. The p-value is Select an answer less than (or equal to) alpha greater than alpha  αα
5. Base on this, we should Select an answer fail to reject the null hypothesis accept the null hypothesis reject the null hypothesis  hypothesis
6. As such, the final conclusion is that...
   • There is sufficient evidence to support the claim that treatment type is a factor in recovery time for pneumonia.
   • There is insufficient evidence to support the claim that treatment type is a factor in recovery time for pneumonia.

Answer 1

Sent Home With Medicine	A Few Hours in the Hospital	Overnight Hospital Stay		Anova: Single Factor
22	8	8
19	15	18		SUMMARY
18	12	18		Groups	Count	Sum	Average	Variance
22	23	4		Sent Home With Medicine	8	175	21.875	25.55357
27	18	5		A Few Hours in the Hospital	9	121	13.44444	28.52778
14	10	10		Overnight Hospital Stay	9	106	11.77778	35.19444
30	18	18
23	8	8
	9	17		ANOVA
				Source of Variation	SS	df	MS	F	P-value	F crit
				Between Groups	487.8088	2	243.9044	8.146051	0.002115	3.422132
				Within Groups	688.6528	23	29.94143
				Total	1176.462	25

Test statistic=Value of F=8.146

p-value=0.0021

There is sufficient evidence to support the claim that treatment type is a factor in recovery time for pneumonia.