In these two exercises, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the Original claim. Use the P-value method unless your instructor specifies otherwise.
Analysis of Last Digits Analysis of the last digits of sample data values sometimes reveals whether the data have been accurately measured and reported. When single digit 0 through 9 are randomly selected with replacement, the mean should be 4.50 and the standard deviation should be 2.87. Reported data (such as weights or heights) are often rounded so that the last digits include disproportionately more 0s and 5s. Use the last digits in the reported lengths (in feet) of the 73 home runs hit by Barry Bonds in 2001 to test the claim that they come from a population with a mean of 4.5. Use a 0.05 significance level. The 73 home-run distances (listed in Data Set 17 in Appendix B) have last digits with a mean of 1.753. Based on the results, does it appear that the distances were accurately measured?
World's Smallest Mammal The world's smallest mammal is the bumblebee bat, also known as the Kitt's hog-nosed bat (or Craseonycteris thonglongyai). Such bats are roughly the size of a bumblebee. List below are weights (in grams) from a sample of these bats. Assuming that the weights of all such bats have a standard deviation of 0.30 g, use a 0.05 significance level to test the claim that these bats are from the same population with a know mean of 1.8 g. Do the bats appear to come from the same population?
1.7 1.6 1.5 2.0 2.3 1.6 1.6 1.8 1.5 1.7 2.2 1.4 1.6 1.6 1.6
The solution identifies the null hypothesis, alternative hypothesis, test statistic, p-value, critical value and conclusion about the null hypothesis. The expert uses the P-value method.