The mean lifetime for cardiac stents is 8.9 years. A medical device company has

Question

The mean lifetime for cardiac stents is 8.9 years. A medical device company has implemented some improvements in the manufacturing process and hypothesizes that the lifetime is now longer. A study of 40 new devices reveals a mean lifetime of 9.7 years with a standard deviation of 3.4 years. Is there statistical evidence of a prolonged lifetime of the stents? Run the test at a 5% level of significance.

Step 1.   Set up hypotheses and determine level of significance   

1) H0: = __?__      2) H1:   >  __?__      3) Level of significance:   =  __?__        

Step 2: Select the appropriate test statistic for a one sample, continuous outcome (the sample size is considered large at >30), so,

Step 3:  Setup decision rule: 4) Reject H0 if Z >  __?__    (Appendix Table 1C: "Z-Values for Hypothesis Tests" - this is a upper-tailed test because H1:   > __ )

Step 4.  Compute the test statistic.

Step 5.  Conclusion.  6) Do or Do Not ?     reject H0 because 7) _____?_____  

8) There is or is not ?   statistically significant evidence at = 0.05 to show that the lifetime is longer than 8.9 years?

Explanation / Answer

1.

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   8.9  
Ha:    u   >   8.9   [ANSWER]

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2.

We use Z DISTRIBUTION as n > 30.

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3.
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha =    0.05          
zcrit =    +   1.645

Hence, we reject Ho when z > 1.645. [ANSWER]

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4.

Getting the test statistic, as              
              
X = sample mean =    9.7          
uo = hypothesized mean =    8.9          
n = sample size =    40          
s = standard deviation =    3.4          
              
Thus, z = (X - uo) * sqrt(n) / s =    1.488130664 [ANSWER]

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5.

6. WE DO NOT REJECT HO because

7. z < 1.645.

8. There is NO significant evidence at alpha = 0.05 to show that the lifetime is longer than 8.9 years. [CONCLUSION]

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