A hospital wants to determine if the type of treatment for pneumonia is a factor

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.

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 0.05.

Ha: At least two of the means are different from each other.

Calculate the p-Value.

p-Value = [ Select ] ["0.0140", "0.4587", "0.0319", "0.6982"] Round to three decimal places

Conclusion: [ Select ] ["There is insufficient evidence to support the claim that at least two of the mean recovery times differ from each other.", "There is sufficient evidence to support the claim that at least two of the mean recovery times differ from each other."]

Overnight Hospital Stay A Few Hours in the Hospital Sent Home with Medicine 14 15 21 18 16 17 12 6 9 24 10 28 6 15 24 8 18 11 26

Explanation / Answer

The statistical software output for this problem is:

Analysis of Variance results:
Data stored in separate columns.

Column statistics

ANOVA table

Hence,

p - Value = 0.0319

p - value is less than 0.05 so reject Ho. Hence,

There is sufficient evidence to support the claim that at least two of the mean recovery times differ from each other.

Column n Mean Std. Dev. Std. Error Overnight Hospital Stay 5 14.8 6.7230945 3.0066593 A Few Hours in the Hospital 7 11.571429 3.8668309 1.4615247 Sent Home with Medicine 7 20.428571 6.4512826 2.4383556

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