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Answer:
We conclude that the true mean life of a biomedical device is greater than 5200 hours.
Step-by-step explanation:
We are given that the life in hours of a biomedical device under development in the laboratory is known to be approximately normally distributed. For this a random sample of 15 devices is selected and found to have an average life of 5323.8 hours and a sample standard deviation of 220.9 hours.
We have to test that the true mean life of a biomedical device is greater than 5200 or not.
Let, Null Hypothesis, :
5200 {means that the true mean life of a biomedical device is less than or equal to 5200 hours}
Alternate Hypothesis, :
> 5200 {means that the true mean life of a biomedical device is greater than 5200 hours}
The test statistics that will be used here is;
T.S. = ~
where, Xbar = sample average life = 5323.8 hours
s = sample standard deviation = 220.9 hours
n = sample devices = 15
So, test statistics = ~
= 2.171
Since, we are not given with the significance level, so we assume it to be 5%, now the critical value of t at 14 degree of freedom in t table is given as 1.761. Since our test statistics is more than the critical value of t which means our test statistics will lie in the rejection region. So, we have sufficient evidence to reject our null hypothesis.
Therefore, we conclude that the true mean life of a biomedical device is greater than 5200 hours.