STA 2023 Lecture Notes - Lecture 30: Confidence Interval, Interval Estimation, Bias Of An Estimator

Consider the following sample of observations on coating thickness for low-viscosity paint. ("Achieving a Target Value for a Manufacturing Process: A Case Study," J. of Quality Technology, 1992:22-26):

Assume that the distribution of coating thickness is normal (a normal probability plot strongly supports this assumption).

(a) Calculate a point estimate of the mean value of coating thickness, and state which estimator you used.

(b) Calculate a point estimate of the median of the coating thickness distribution, and state which estimator you used.

(c) Calculate a point estimate of the value that separates the largest 10% of all values in the thickness distribution from the remaining 90% and state which estimator you used. [Hint: Express what you are trying to estimate in terms of m and s]

(d) Estimate P(X<1.5), i.e., the proportion of all thickness values less than 1.5 [Hint: if you know the values of and , you could calculate this probability. These values are not available , but they can be estimated.]

(e) What is the estimated standard error of the estimator that you used in part (b)?

1. A sample of size n=49 is drawn from a population whose standard deviation is .

(a) Find the margin of error for a 95%confidence interval for .

b) If the sample size were n=60, would the margin of error be larger would be larger or smaller.

2.  Determine the point estimate of the population mean and margin of error for the confidence interval. The lower bound is 23; the upper bound is 27. The point estimate of the population mean is? The margin of error for the confidence interval is?

The ages of a group of

randomly selected adult females have a standard deviation of

years. Assume that the ages of female statistics students have less variation than ages of females in the general​ population, so let

years for the sample size calculation. How many female statistics student ages must be obtained in order to estimate the mean age of all female statistics​ students? Assume that we want

confidence that the sample mean is within​ one-half year of the population mean. Does it seem reasonable to assume that the ages of female statistics students have less variation than ages of females in the general​ population?