The Newton Scientific Instrument Company manufactures scales with its day shift and night shift. Random samples are routinely tested with errors recorded as positive amounts for readings that are too high or negative for readings that are too low.
a. A random sample of 40 scales made by the day shift is tested and the errors are found to have a mean of 1.2 g and a standard deviation of 3.9 g. Use a 0.05 significance level to test the claim that the sample comes from a population with a mean error equal to 0.
b. A random sample of 33 scales made by the night shift is tested and the errors are found to have a mean of - 1.4 g and a standard deviation of 4.3 g. Use a 0.05 significance level to test the claim that the sample comes from a population with a mean error equal to 0.
c. Use a 0.05 significance level to test the claim that both shifts manufacture scales with the same mean error.
d. Construct a 95% confidence interval for the mean error of the day shift.
e. Construct a 95% confidence interval for the mean error of the night shift.
f. Construct a 95% confidence interval for the difference between the means of errors for the day shift and night shift.
g. If you want to estimate the mean error for the day shift, how many scales must you check if you want to be 95% confident that your mean is off by no more than 0.5 g? (Hint: Use the sample standard deviation in part (a) as an estimate of the population standard deviation cr.)