Give an Example of a Hypothesis Test You Could Perform at Work Or at Home. State What The

Give an example of a hypothesis test you could perform at work or at home. State what the Null and the Alternative hypotheses would be in your test. Explain how you would settle on a reasonable level of significance for your scenario. Also explain what the type I and II errors would be if you reached the incorrect conclusion in your test.

Hypothesis Test at the Work Place:
Imagine that you work in the Standards Department of a large hospital and part of your work also calls for assisting the Planning Department. There is proposal to have more beds in some wards. The Planning Department Manager has asked you to make a study and advice if new beds need to be added in the Advanced Surgery ward.
To start with the analysis, you have collected the data on the mean hospital stay for Advanced Surgery patients and that for Conventional Surgery patients. You summarize the data s follows:
Sample / Sample size / Mean / Standard deviation
Advanced / 48 / 5.5 days / 1.5 days
Conventional / 55 / 8.0 days / 2.0 days
You would like to conduct a hypothesis test to answer the research question: Is the mean hospital stay for advanced surgery patients less than the mean hospital stay for conventional surgery patients?.
Since the matter involves patient care, you settle for a tight level of significance of α = 0.01
As you conduct the test, you make the following notes:
a. What is the significance level? 1% (α = 0.01)
b. What are the sample means? x1-bar = 5.5 and x2-bar = 8.0
c. What are the corresponding sample standard deviations? s1 = 1.5 and s2 = 2
d. What are the corresponding sample sizes? n1 = 48 and n2 = 55
e. What is the value of the null value? 0
f. Express the null hypothesis verbally and mathematically.
Ho:The mean hospital stay for advanced surgery patients is the same as or greater than the mean hospital stay for conventional surgery patients, that is μ1 - μ2 ≥ 0
g. Express the alternative hypothesis mathematically.
Ha: The mean hospital stay for advanced surgery patients is less than the mean hospital stay for conventional surgery patients, that is μ1 - μ2 < 0
h. Determine the value of the standard error.
Pooled SD, s = √[{(n1 - 1) s1^2 + (n2 - 1) s2^2} / (n1 + n2 - 2)] = 1.78484
SE = s * √{(1 /n1) + (1 /n2)} = 0.35255
i. Determine the degrees of freedom. n1 + n2 - 2 = 101
j. Determine the value of the test statistic. t = (x1-bar - x2-bar)/SE = -7.09128
k. Determine the 0
l. Is this test statistically significant? Specifically, why or why not?
Yes, because the p- value (0) < α (0.01)
m. What conclusion(s) can you make about the null and alternate hypotheses?
We reject Ho and accept Ha
n. Interpret the results.
It appears that the mean hospital stay for advanced surgery patients is less than the mean hospital stay for conventional surgery patients
o. What is the recommendation?.
Since the mean hospital stay for advanced surgery patients is less than the mean hospital stay for conventional surgery patients, more beds should be planned in the Conventional Surgery ward rather than in the Advanced Surgery ward.
p. What could be the Type I error?
In reality, the mean hospital stay for advanced surgery patients is the same as or greater than the mean hospital stay for conventional surgery patients, but you reject this fact on the basis of the hypothesis test
q. What could be the Type II error?
In reality, the mean hospital stay for advanced surgery patients less than the mean hospital stay for conventional surgery patients, but you fail to reject this fact on the basis of the hypothesis test