A researcher wants to examine how shift durations of medical residents impact me

Question

A researcher wants to examine how shift durations of medical residents impact medical errors. She classifies residents based upon the number of long-duration (24 hr) shifts per month that they work (0-4 long-duration shifts and 5 long-duration shifts per month), and records how many medical errors they have in a one-month period. Below are the data from 25 medical residents. Do medical residents who have 5+ long-duration shifts per month make significantly more medical errors than residents who have 0-4 long-duration shifts/month? Test at =0.05.

0-4 long-duration shifts/month

5+ long-duration shifts/month

Number of medical errors in one month

0-4 long-duration shifts/month

5+ long-duration shifts/month

Number of medical errors in one month

0 2 3 1 2 5 0 4 5 2 2 0 4 6 0 2 1 1 1 0 3 2 4 4 4

Explanation / Answer

Let

u1 = mean of 5+
u2 = mean of 0-4

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   <=   0  
Ha:   u1 - u2   >   0  
At level of significance =    0.05          
As we can see, this is a    right   tailed test.      
Calculating the means of each group,              
              
X1 =    2.272727273          
X2 =    2.357142857          
              
Calculating the standard deviations of each group,              
              
s1 =    1.954016842          
s2 =    1.736802671          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    11          
n2 = sample size of group 2 =    14          
Thus, df = n1 + n2 - 2 =    23          
Also, sD =    0.750047029          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    -0.112547055          
              
where uD = hypothesized difference =    0          
              
Now, the critical value for t is              
              
tcrit =    +   1.713871528      
              
As t < 1.714,   WE FAIL TO REJECT THE NULL HYPOTHESIS.          

Hence, there is no significant evidence that medical residents who have 5+ long-duration shifts per month make significantly more medical errors than residents who have 0-4 long-duration shifts/month. [CONCLUSION]

**************************

Hi! In fact, in this sample, the mean of 5+ is even less than 0-4. That means from the very start, we know the result that there is no evidence that the mean of 5+ is not greater than 0-4.

*****************************************************

Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.