Question

In a poll of 14,697 randomly selected adults in the United States, those polled spent an average of $95 per day in November of last year, as compared with $91 per day in November two years ago. The estimates had a margin of error of $4 at the 95% confidence level. Which of the following is a reasonable claim to make based on this sample?

Answer 1

Based on the margin of error and confidence level, a reasonable claim is that there is evidence of an increase in average daily expenditure, but the claim should acknowledge the range of plausible values due to the margin of error.

Step-by-step explanation:

In the poll of 14,697 randomly selected adults in the United States, we see that the average daily expenditure in November last year was $95 with a margin of error of $4 at the 95% confidence level. This figure is compared with $91 per day from November two years ago. Based on the provided margin of error, we can reasonably claim that the true mean of the daily expenditure for the adult population in the U.S. during November of last year is likely to be between $91 and $99 (i.e., $95 ± $4). Since the estimated average for two years ago is $91, which is within that range, we cannot conclusively say there was a significant increase in average daily expenditure. However, given that $91 is at the lower end of the confidence interval, it's also reasonable to claim that there is evidence of an increase in spending. Importantly, the margin of error does provide a range of plausible values for the average daily spend, and any claims should acknowledge this uncertainty.

Answer 2

Answer: It is Plausible that average daily spending of adults in the United States remained the same in November of last year as it was in November two years ago -- Khan Academy --

Step-by-step explanation: It is Plausible that average daily spending of adults in the United States remained the same in November of last year as it was in November two years ago