Module 12: Confidence Intervals Part 2 In this module we'll pick up where we left off in Module 11. This module is divided into 2 parts: A. Confidence intervals to estimate the population proportion. B. Confidence intervals to estimate the population variance. Confidence intervals to estimate the population proportion are similar to the previous confidence intervals discussed in Module 11. However, confidence intervals to estimate the population variance are significantly different and require the use of the χ 2 (chi-square) distribution.
Module 12: Confidence Intervals Part 2 A. Confidence intervals to estimate the population proportion When constructing confidence to estimate the population proportion, we use the Z-Distribution used in in Module 11 to estimate the population mean for large sample sizes. This table, from slide 7 in Module 11, is applicable here. As in Module, if you're constructing a confidence interval with a confidence level different from one of the examples in this table, you will need to use Excel to determine the correct factor using the method in the table above and discussed on slide 6 in Module 11. • Confidence α α/2 Z α/2 Z α/2 0.99 0.01 0.005 Z .005 2.5758 =NORMSINV(0.005)*-1 0.98 0.02 0.01 Z .01 2.3263 =NORMSINV(0.01)*-1 0.96 0.04 0.02 Z .02 2.0537 =NORMSINV(0.02)*-1 0.95 0.05 0.025 Z .025 1.9600 =NORMSINV(0.025)*-1 0.90 0.10 0.05 Z .05 1.6449 =NORMSINV(0.05)*-1 0.85 0.15 0.075 Z .075 1.4395 =NORMSINV(0.075)*-1 0.80 0.20 0.10 Z .10 1.2816 =NORMSINV(0.1)*-1
Module 12: Confidence Intervals Part 2 A. Confidence intervals to estimate the population proportion The formula for constructing confidence intervals to estimate the population proportion is as follows: ± Where: = the sample proportion. If is not given, is calculated by = = 1 - n = sample size (as always) 1= the Z-Factor as explained on the previous slide and in Module 11. Confidence intervals to estimate the population proportion are very straightforward. The only issue is whether the sample proportion () is given or not, in which case = is the point estimate for the population proportion is the confidence interval half width •
Module 12: Confidence Intervals Part 2 A. Confidence intervals to estimate the population proportion Example 1 : A study of 87 randomly selected companies with a telemarketing operation was completed. The study revealed that 39% of those sampled had used telemarketing to assist them in order processing. Use this information to construct a 95% confidence interval for the population proportion of telemarketing companies that use their telemarketing operation to assist them in order processing. [We know this is a proportion problem rather then a mean problem since it's asking you to construct a confidence interval for the population proportion as opposed to constructing a confidence interval for the population mean as we did in Module 11. Always read the questions carefully so you don't get things confused] From the text we know the following: is given and = .39; = .61 (1 - .39 = .61); n = 87; and that with a 95% level of confidence, α/2 = .025.
- Spring '14
- Normal Distribution, BURGER KING, α