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 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 = ___?___ [a]

b) H₁:  μ > ___?___ [b]

c)  α =  ___?___  [c]   

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  > ___?___ [d] (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: ___?___  [e]

Step 5.  Conclusion.  

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

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

Answer 1