Question

What sample size, including the 20 observations in the initial study, would be necessary to have a confidence of 95.44 percent that the observed time was within 4 percent of the true value?

Answer 1

Completed question:

An initial time study resulted in an average observed time of 2.2 minutes per cycle, and a standard deviation of .3 minutes per cycle. The performance rating was 1.20. What sample size, including the 20 observations in the initial study, would be necessary to have a confidence of 95.44 percent that the observed time was within 4 percent of the true value?

Answer:

47

Step-by-step explanation:

When doing a statistic study, a sample of the total amount must be taken. This sample must be done randomly, and, to be successful, the sample size (n) must be determined, by:

$n = (\frac{Z_{\alpha/2}*S }{E})^2$

Where Z(α/2) is the value of the standard normal variable associated with the confidence, S is the standard deviation, and E is the precision. The confidence indicates if the study would have the same result if it would be done several times. For a confidence of 95.44, Z(α/2) = 2.

The standard deviation indicates how much of the products deviate from the ideal value, and the precision indicates how much the result can deviate from the ideal. So, if it may vary 4% of the true value (2.2), thus E = 0.04*2.2 = 0.088.

n = [(2*0.3)/0.088]²

n = 46.48

n = 47 observations.