a. Anthropologists have discovered a prehistoric cave dwelling that contains a large number of adult human footprints. To study the size of the adults who used the cave dwelling, they randomly selected 20 of the footprints from the population of all footprints in the cave and measured the length of those footprints. Some statistics resulting from this random sample are as follows.

Sample size: 30

Mean: 24.8cm

Standard deviation: 7.5cm

Minimum 15.2

First Quartile: 18.7

Median: 21.5

Third Quartile: 30.0cm

Maximum 37.0cm

a. The anthropologists would like to construct a 95 percent confidence interval for the mean foot lengths of the adults who used the cave dwelling. Construct that 95% confidence interval and interpret the confidence interval as it relates to the problem. (Briefly list off and check the assumptions since you can use your notes on this assignment.)

b. If we assume that the standard deviation of footprints is in fact 7.5 centimeters, and we want to construct a 98% confidence interval with a margin of error of less than 2.5 centimeters, at least how many footprints will we need to analyze?

1. The anthropologists would like to construct a 95 percent confidence interval for the mean foot lengths of the adults who used the cave dwelling. Construct that 95% confidence interval and interpret the confidence interval as it relates to the problem. (Hint: List out the steps of PANIC to help you through the process. Briefly list off and check the assumptions since you can use your notes on this assignment.)