Question

1. The mean lifetime for cardiac stents is 8.9years. 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 a hypothesis test at α = 0.05 level of significance using the 5-Step Approach:

   Step 1.   Set up hypotheses and determine level of significance   

   a) H₀: μ = ___?___

   b) H₁:  μ > ___?___  

   c)  α =  ___?___     

   Step 2: Select the appropriate test statistic for a one sample, continuous outcome and we'll state the sample is "large" at 40, so let's try the z-test statistic:

     { = 9.7,  = 8.9, s = 3.4, n (sample size) = 40}

   Step 3:  Setup decision rule:  

   d) Reject H₀ if Z  > ___?___   (this is an upper-tailed test because H₁: μ  > __ )

   Step 4.  Compute the test statistic.  

   e)    =  plug the numbers into the calculation to get the final answer: ___?___  

   Step 5.  Conclusion.  

   f & g) Reject or Fail to Reject H₀ ___?___ ,  because ___?___  < 1.645

   h) There is or There is not ___?___  statistically significant evidence at α = 0.05 to show that the stent lifetime is longer than 8.9 years.

Answer 1

step 1:

null hypothesis:Ho μ	=	8.9
Alternate Hypothesis:Ha μ	>	8.9

c)alpha =0.05

step 2:

population mean μ=	8.9
sample mean 'x̄=	9.700
sample size    n=	40.00
std deviation σ=	3.40
std error ='σx=σ/√n=	0.5376
test stat z = '(x̄-μ)*√n/σ=	1.49

  Reject H0 if Z  > 1.645

Step 4.  Compute the test statistic =1.49

Step 5.  Conclusion.   Fail to Reject H0 beayuse z< 1.645

h)

There is not  statistically significant evidence at α = 0.05 to show that the stent lifetime is longer than 8.9 years