Question

A machine produces metal rods used in an automobile suspension system. a random sample of 15 rods is selected and the diameter is measured. the resulting data (in millimeters) are as follows: no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 dia. 8.21 8.19 8.23 8.25 8.26 8.23 8.20 8.26 8.19 8.23 8.20 8.28 8.24 8.25 8.24 use the data above to calculate a 95% two-sided confidence interval on the mean rod diameter. assume the data are normally distributed. (a) calculate the sample mean and standard deviation. round the sample mean and the sample standard deviation to 2 and 3 decimal places respectively (e.g. 98.76 and 98.765).

Answer 1

a) Sample mean is obtained by adding all 15 numbers, and dividing by 15. This gives an answer of 8.2307
To find SD, we would subtract one of the data points from the mean and square the value. We would have to add up all the squared differences for all 15 points, which would be the variance. Then we take the square root to get 0.028 (to 3 decimal places). To 2 decimal places, this is 0.03.

b) 95% Confidence Interval: For two-sided CI, the corresponding z-factor is 1.96. Then the bounds are:
Lower bound = mean - z*SD = 8.2307 - 1.96*0.028 = 8.17582
Upper bound = mean + z*SD = 8.2307 + 1.96*0.028 = 8.28558
So the confidence interval is (8.176, 8.286).