Sample data: 4.4 5.0 5.9 4.4 4.8 4.2 4.7 3.2 5.5 a. What is the sample mean? b.

Question

Sample data: 4.4 5.0 5.9 4.4 4.8 4.2 4.7 3.2 5.5

a. What is the sample mean?

b. What is the die life sample standard deviation?

c. What is the standard error of the sample mean?

d. What is the point estimate for the population mean?

e. To find that 95% confidence interval estimate for the population mean die life in days, the correct critical value (interval coefficient) to use is:

f. Report the margin of error (confidence bound) for a 95% confidence interval estimate for the population mean die life in days:

g. Report the 95% lower and upper confidence limits for your estimate of the population mean:

h. Make a statement to interpret your confidence interval estimate.

i. The operations manager has adjusted the pressure of the injection material on all machines and now claims the mean die life is at least 4 production days. Do your previous findings support or refute his claim and why?

Explanation / Answer

(a) Sample Mean is 4.677778

(b) Sample Deviation formula is s = Sqrt( Sum( Xi -Sample mean)^2/(n-1))

    Sample Standard deviation is 0.779066

(c)Standard error of sample mean = s/sqrt(n)=0.779066/3=0.259688666

(d) the sample mean is a point estimate of the population mean

   so the point estimate for the population mean is same as the Sample Mean which is 4.677778

(e) the 95% confidence interval for population mean is   4.079 to 5.277

the confidence interval formula is ( sample mean-(tn-1).s/sqrt(n) , sample mean + tn-1.s/sqrt(n)) with n-1 degrees of freedom

(f) Margin of error is ME = Critical value x Standard error

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