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Statistics Help

**Question: **You have obtained the number of credit hours of ongoing education from one random sample of 48 physicians from Hospital A and the number of credit hours of ongoing education from a second random sample of 40 physicians from Hospital B. The average credit hours of ongoing education for the sample from Hospital A is 50 credit hours with a standard deviation of 6.2 credit hours. The average credit hours of ongoing education for the sample from Hospital B is 58 credit hours with a standard deviation of 5.4 credit hours. Is there a statistically significant difference between the credit hours earned of physicians in Hospital A and Hospital B? Assume these are Independent samples.

(Hint: Continuous Variable, Normally distributed – both of these could have been left out and you could have recognized it. We know we can use Normal distribution because of large sample size. The previous sample size cutoff shown in the class was 40, but really 99% of the time you can assume the normal distribution at any sample size >30.)

(A) State the Null and Alternative Hypotheses

(B) Calculate the test statistic (Provide answers for all intermediate steps)

(C) Assess the null hypothesis and interpret the results. (Hint: we do not really know the purpose of the study so there is limited interpretation) Edit

**Answer: **A. Null hypothesis : H0: mu_1 = mu_2

Alternative Hypothesis : H1: mu_1 ≠ mu_2

B.

xbar_1=50 , xbar_2=58

n_1=48 , n_2=40

s_1=6.2 , s_2=5.4

Standard error= sqrt({(s_1)^2/n_1}+{ (s_2)^2}/n_2})=sqrt(6.2^2/48 + 5.4^2/40)=1.2368

Test statistic, z= [(xbar_1 -xbar_2)/standard error]=(50-58)/1.2368=-6.47

.01 level -------> zcritical = ± 2.58

|zcalculated |≥ |zcritical| (because 6.47>2.58)

C. Significance!

Reject Null

Restate Alternative

Yes, there a statistically significant difference between the credit hours earned of physicians in Hospital A and Hospital B.

Edit

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