Class Exercise 11

Problem 1

A small brewery monitors the alcohol content of its beer by taking $6$ samples from every vat brewed. The following are the percent alcohol content data for the sample taken from tha last vat:$$ 5.3 \;\; 5.0\;\; 5.1\;\; 5.4\;\; 5.3\;\; 5.3$$
  1. Calculate the mean and the standard deviation for the alcohol content of the sample.
  2. Assuming the population is approximately normally distributed construct a $98\%$ confidence interval for the mean alcohol content.

Problem 2

A researcher believes that in recent years women have been getting taller. She knows that $10$ years ago the average height of young adult women living in her city was $63$ inches. The standard deviation is unknown. She randomly samples eight young women residing in her city and measures their heights. The following data is obtained:$$64\;\; 66\;\; 68\;\; 60\;\; 62\;\; 65\;\; 66\;\; 63$$Based on this sample, can the reasearcher state with $95\%$ confidence that the average height of women changed in the past $10$ years? Assume the population is approximately normal.