DuToit, hansen and osborne measured the diameters of some no. 10 machine screws with two different calipers (digital and vernier scale). Part of their data are recorded here. Given in the small frequency table are the measurements obtained on 50 screws by one of the students using the digital calipers. A) Compute the sample mean and standard deviation for these data.
Diameter Frequency
4.52 1
4.66 4
4.67 7
4.68 7
4.69 14
4.70 9
4.71 4
4.71 4
B) Use your sample values from (a) and make a 98% two-sided confidence interval for the mean diameter of such screws as measured by this students with these calipers.
C) Repeat part (b) using 99% confidence. How does this interval compare with the one from (b)?
D) Use your values from (a) and find a 98% lower confidence bound for the mean diameter. How does this value compare to the lower endpoint of your interval from (b)?
E) Repeat part (d) using 99% confidence. How does the value computed here compare with your answer for (d)?
F) Interpret your interval from (b) for someone with little statistical background.