Answer:
a) The evidence suggest the true mean life of a biomedical device > 5500
b) (5487.94, +∞)
c) There is evidence to support that the mean is equal to 5500
Step-by-step explanation:
Here we have
(a) To test the hypothesis we have the claim that the mean life of biomedical devices > 5500
Therefore, we put the null Hypothesis which is the proposition that a difference does not exist. That is
H₀: μ = 5500
Therefore, the alternative hypothesis will be
Hₐ: μ > 5500
The test statistic is then found by;
The P value from the T table at df = n - 1 = 15 - 1 = 14 is
0.025 < P < 0.05
The P value is given as 0.036 from the T distribution at 14 derees of freedom df
Therefore, since P < α or 0.05, we reject the null hypothesis. That is we fail to reject Hₐ: μ > 5500. The evidence suggest the true mean life of a biomedical device > 5500
(b) The 95% confidence interval is given as
Which gives t =
2.145
The confidence interval of the lower bound on the mean is then
(5487.94, +∞)
c) From the above result, we find that the mean of 5500 is contained in the range of the lower confidence on the mean. We can therefore, accept the null hypothesis. That is there is evidence to support that the mean is equal to 5500.