Researchquestion
Supposingthat we wish to look at the Virginia hospitals’ total surgeries asa single variable and state a hypothesis as follows:
Hypothesis
H_{1:}The mean number of surgeries has increased significantly between 2001and 2005 that is
H_{1:}x >µ
H_{O}:The null hypothesis is that the mean number of total surgeriesperformed at Virginia hospitals has not increased between 2001 and2005
H_{O}😡 = µ
TypeI error
Thiswill be done if we reject the hypothesis H_{1}when it should be accepted hence giving a false positive[ CITATION Owe811 l 1033 ].
TypeII error
Acceptingthe hypothesis H_{1:} when it should be rejected
TypeI error:
Rejectingthat the number of surgeries has increased significantly when weshould have accepted that the number actually increased significantly
TypeII error
Acceptingthat the number of surgeries has increased significantly whenactually the number of surgeries has not increased significantly
Inthe data on the Virginia hospitals, the tests performed indicatedthat the mean surgeries in 2005 had a t statistic of 1.49 which waswithin the limits at 95% confidence level as shown in the tablebelow.
tTest: Paired Two Sample for Means 

  
Total surgeries01 
Total surgeries05 
Mean 
8527.555556 
8979.777778 
Variance 
76465087.8 
88652283.03 
Observations 
81 
81 
Pearson Correlation 
0.957479361 

Hypothesized Mean Difference 
0 

df 
80 

t Stat 
1.490920111 

P(T<=t) onetail 
0.069957541 

t Critical onetail 
1.664124579 

P(T<=t) twotail 
0.139915083 

t Critical twotail 
1.990063387 
not significant 
Theconclusion from the analysis would be that we reject the hypothesisH_{1}and accept the null hypothesis H_{o}. Therefore the mean total number of surgeries in Virginia Hospitalshas not increased significantly between 2001 and 2005 at 95%confidence level.
Committinga type one error in this case would mean that the mean of 8979obtained in 2005 is significantly different yet we have said that itis not significantly different from the mean of 8527 in 2001 (falsepositive).
Committinga type II error in this case would mean that the mean of 8979obtained in 2005 is not significantly different from the mean of 8527in 2001 yet it is actually significantly different.
Iftype I error is committed, it would imply that surgeries have moreand we would mobilize more resources towards performing surgeries inthe hospitals when it is actually not necessary.
Iftype II error is committed, we would think that the surgeries haveenough resources and are properly taken care of or managed when weactually need to put more resources there to contain an increaseddemand [ CITATION Ind13 l 1033 ]. This is very important especially in cases that need absolutecorrectness like surgery.
Familywise error rate
Thisis the probability of at least one type of type I error (falsepositive) occurring. In our case, it is possible to have a Type Ierror occurring and therefore family wise error rate should beconsidered and controlled [ CITATION Ake08 l 1033 ]. There are many several ways of controlling family wise error rateusing the p values. Such probability checks would also helpmanagement in checking out that a decision they are making isrelevant and necessary and statistically reliable.
References
Akey. (2008). Washington education. Retrieved December 4, 2014, from gs website: http://www.gs.washington.edu/academics/courses/akey/56008/lecture/lecture10.pdf
Indrayan, A. (2013). SensitivitySpecificity. AITBS , 400.
Owen, F., & Etal. (1981). Statistics. London: Polytech.