In a national poll of 1039 U.S. adults, conducted November 7-10, 2013, Gallup asked "Roughly how much money do you think you personally will spend on Christmas gifts this year?". The data provided on the WeissStats site are based on the results of the poll.
a. Determine a 95% upper confidence bound for the mean amount spent on Christmas gifts in 2013. (Note: The sample mean and sample standard deviation of the data are $704.00 and $477.98, respectively.)
b. Interpret your result in part (a).
c. In 2012, the mean amount spent on Christmas gifts was $770.
Comment on this information in view of your answer to part (b).
8.151 Bootstrap Confidence Intervals. With the advent of highspeed computing, new procedures have been developed that permit statistical inferences to be performed under less restrictive conditions than those of classical procedures. Bootstrap confidence intervals constitute one such collection of new procedures. To obtain a bootstrap confidence interval for one population mean, proceed as follows.
1. Take a random sample of size n (the sample size) with replacement from the original sample.
2. Compute the mean of the new sample.
3. Repeat steps 1 and 2 a large number (hundreds or thousands) of times.
4. The distribution of the resulting sample means provides an estimate of the sampling distribution of the sample mean. This estimate is called a bootstrap distribution.
5. The (estimated) endpoints of a 95% confidence interval for the population mean are the 2.5th and 97.5th percentiles of the bootstrap distribution (i.e., P2.5 and P97.5).
Refer to Example 8.10 on page 356. Use the technology of your choice to find a 95% bootstrap confidence interval and compare your result with that found by using the one-mean t-interval procedure. Discuss any discrepancy that you encounter.