Five toothpaste tubes were squeezed until empty and weighed to measure the amount remaining. The average amount remaining was 0.49 ounces, which is less than the 10% of contents that is advertised. A hypothesis test was conducted at a 5% significance level to determine if the true average is less than 10% of the advertised amount. Type I and II errors could occur and depending on the significance level used, the conclusion could change.

1. Suppose five 6 oz tubes of toothpaste are randomly selected and squeezed until no more
toothpaste will come out. Then each tube is cut open and the amount remaining is weighed,
resulting in the following data. 0.53, 0.65, 0.46, 0.5, 0.37. Does it appear that the true average
amount left is less than 10% of the advertised contents?
A. check the validity of any assumptions necessary for testing the appropriate hypotheses.
B. carry out a test of the appropriate hypotheses using a significance level of 0.05. Would your
conclusion change if a significance level of 0.01 had been used?
C. decribe in context type I and type II errors, and say which error might have been made in
reaching a conclusion?
Solution
http://www.stats.gla.ac.uk/steps/glossary/hypothesis_testing.html#hypothtest
http://statistics.about.com/od/Inferential-Statistics/a/An-Example-Of-A-Hypothesis-Test.htm