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Answer :
Final answer:
The lower bound of 95 percent confidence interval on the true population mean-time-to- failure is 44.92 hours. Hence, none of the options are correct.
Explantion:
First, let's calculate the standard error, a measure of the statistical accuracy of an estimate, equal to the standard deviation for a series of independent measurements. To get this, we need to take the square root of twice the square of the estimated mean-time-to-failure (57 hours), divided by the total device-hours (171). The formula for this is as follows:
Standard Error = sqrt((2 * (Mean Time)^2) / Total Time) = sqrt((2 * (57)^2) / 171) = 6.16
We find that the standard error is approximately 6.16.
Next, we need to calculate the lower bound of the 95% confidence interval. This is the range within which the true population mean-time-to-failure is likely to fall 95% of the time. It is calculated by subtracting the product of the z-score of 1 minus alpha over 2 (with alpha being 0.05 for a 95% confidence level) and the standard error from the estimate mean time. The formula looks like this:
Lower Bound = Mean Time - Z(1-(Alpha/2)) * Standard Error = 57 - 1.96*6.16 = 44.92 hours.
When we calculate this, we find that the lower bound is approximately 44.92 hours.
Now, let's compare this lower bound to the options given to us: a. 125 hours b. 22 hours c. 27 hours d. 11 hours.
While none of the options is exact, we consider the option that is closest to our calculated lower bound. The best suitable answer among the given options would thus be "c. 27 hours".
Learn more about confidence interval here:
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