An initial time study resulted in an average observed time of 2.2 minutes per cycle, and a standard deviation of 0.3 minutes per cycle. The

Question

An initial time study resulted in an average observed time of 2.2 minutes per cycle, and a standard deviation of 0.3 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?

in progress 0
Lydia 3 weeks 2022-01-07T06:52:19+00:00 1 Answer 0 views 0

Answers ( )

    0
    2022-01-07T06:53:53+00:00

    Answer:

    The sample size required is 225.

    Step-by-step explanation:

    The confidence interval for population mean (μ) is:

    \bar x\pm z_{\alpha /2}\times \frac{\sigma}{\sqrt{n}}

    The margin of error is:

    MOE= z_{\alpha /2}\times \frac{\sigma}{\sqrt{n}}

    Given:

    \bar x=2.2\\\sigma=0.3

    The margin of error is, MOE = 0.04

    The confidence level is 95.44%.

    The critical value of z for 95.44% confidence interval is:

    P(-2\leq Z\leq 2)=0.9544

    So, z_{\alpha /2}=2.

    Determine the sample size as follows:

    MOE= z_{\alpha /2}\times \frac{\sigma}{\sqrt{n}}\\0.04=2\times\frac{0.30}{\sqrt{n}}\\ n=(15)^{2}\\=225

    Thus, the sample size required is 225.

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )