1. If you want to be 95% confident of estimating the population portion to within a sampling error of + 0.02 and there is historical evidence that the population proportion is approximately 0.40, what sample size is needed?
2. In a study of 500 executives, 315 stated that their company informally monitored social networking sites to stay on top of information related to their company .
a. Construct a 95% confidence interval for the proportion of companies that informally monitored social networking sites to stay on top of information related to their company.
b. Interpret the interval constructed in (a).
c. If you wanted to conduct a follow-up study to estimate the population proportion of companies that informally monitored social networking sites to stay on top of information related to their company to within + 0.01 with 95% confidence, how many executives would you survey?
3. The real estate assessor for a county government wants to study various characteristics of single-family houses in the county. A random sample of 70 houses reveals the following:
Heated area of the houses (in square feet): X= 1,759, S=380
42 houses have central air-conditioning
a. Construct a 99% confidence interval estimate for the population mean heated area of the houses.
b. Construct a 95% confidence interval estimate for the population proportion of houses that have central air-conditioning.
4. A quality characteristic of interest for a tea-bag filling process is the weight of the tea in the individual bags. In this example, the label weight on the package indicates that the mean amount is 5.5 grams of tea in a bag. If the bags are under filled, two problems arise. First, customers may not be able to brew the tea to be as strong as they wish. Second, the company may be in violation of the truth-in-labeling laws. On the other hand, if the mean amount of tea in a bag exceeds the label weight, the company is giving away product. Getting an exact amount of tea in a bag is problematic because of variation in the temperature and humidity inside the factory, differences in the density of the tea, and the extremely fast filling operation of the machine (approximately 170 bags per minute). The following data are the weights, in grams, of a sample of 50 tea bags produced in one hour by a single machine:
5.65 5.44 5.42 5.40 5.53 5.34 5.54 5.45 5.52 5.41
5.57 5.40 5.53 5.54 5.55 5.62 5.56 5.46 5.44 5.51
5.47 5.40 5.47 5.61 5.53 5.32 5.67 5.29 5.49 5.55
5.77 5.57 5.42 5.58 5.58 5.50 5.32 5.50 5.53 5.58
5.61 5.45 5.44 5.25 5.25 5.63 5.50 5.57 5.67 5.36
a. Construct a 99% confidence interval estimate for the population mean weight of the tea bags.
b. Is the company meeting the requirement set forth on the label that the mean amount of tea in a bag is 5.5 grams?
c. Do you think the assumption needed to construct the confidence interval estimate in (a) is valid?
The solution provides step by step method for the calculation of confidence interval and sample size for mean and population proportion. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.