Introduction to Confidence Intervals (page 248)
In chapter 7 we discussed how to make inferences about a population parameter based on a sample statistic. While this can be useful, it has severe limitations. In Chapter 8, we expand our toolbox to include Confidence Intervals. Instead of basing our inference on a single value, a point estimate, a Confidence Interval provides a range of values, an interval, which – at a certain level of confidence (90%, 95%, etc.) – contains the true population parameter. Having a range of values to make inferences about the population provides much more room for accuracy than making an inference off of only one value.
When we worked with probabilities based on sample means, we learned that there is
In order to estimate the mean weight loss of all customers, a nutritionist takes a sample of 18 dieters and records their weight loss one month after joining the program. He computes the sample mean and the standard deviation of weight loss as 12.5 pounds and 9.2 pounds, respectively. He believes that weight loss is likely to be normally distributed.
Calculate the margin of error with 95% confidence.
Df=18-1=17 alpha/2=.025 2.110 x (9.2/sqrt18) = 4.58
Compute the 95% confidence interval for the population mean.
12.5 +(-) 4.58 = [7.92, 17.08]
According to a recent survey based on a random sample of 36 high school girls, high school girls average 100 text messages daily with a standard deviation of 10 text messages daily.
Calculate the margin of error with 99% confidence.
Df=36-1=35 alpha/2= .005 t=2.724 2.724 x (10/sqrt36) = 4.54
What is the 99% confidence interval for the population mean texts that all high school girls send daily?
100 +(-) 4.54 = [95.46, 104.54]
The Chartered Financial Analyst (CFA) designation is fast becoming a requirement for serious investment professionals. Although it requires a successful completion of three levels of grueling exams, it also entails promising careers with lucrative salaries. A student of finance is curious about the average salary of a “CFA” charter