Question

A manufacturing company’s quality control personnel have recorded the proportion of defective items for each of 500 monthly shipments of one of the computer components that the company produces. The data are in the file P07_07.xlsx. The quality control department manager does not have sufficient time to review all
of these data. Rather, she would like to examine the proportions of defective items for a sample of these shipments. For this problem, you can assume that the population is the data from the 500 shipments.

a. Use Excel to generate a simple random sample of size 25 from the data.

b. Calculate a point estimate of the population mean from the sample selected in part a. What is the sampling error, that is, by how much does the sample mean differ from the population mean?

c. Calculate a good approximation for the standard error of the mean.

d. Repeat parts b and c after generating a simple random sample of size 50 from the population. Is this estimate bound to be more accurate than the one in part b? Is its standard error bound to be smaller than the one in part c?

I am not able to attach the Data table as the content is too large to copy paste. Can you please let me know the alternative for this.

Answer 1

a. The random sample size is 25. In excel we use 'RAND( ) ' function to create random numbers, fix these numbers in another column using "Paste special" and "Value" option in excel. Then arrange the data in increasing order, using the column where the random numbers are fixed.

Since there are 500 records, our population consists of N=500 items.

b) The population mean for proportion of defectives is 0.50

The point estimate for sample size of 25 is

The sampling error is 0.57-0.50 = 0.07.

c) The standard error is,