# Testing a Hypothesis using Statistical Data

(1) Test the given claim using the traditional method of hypothesis testing. Assume that the sample has been randomly selected from a population with a normal distribution.

Show a complete hypothesis test with all six steps.

A public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes. A college student took bus number 14 during peak hours on 18 different occasions. Her mean waiting time was 7.4 minutes with a standard deviation of 1.7 minutes. At the 0.01 significance level, test the claim that the mean is less than 10 minutes.

(2) Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected.

Show a complete hypothesis test with all six steps.

A machine dispenses a liquid drug into bottles in such a way that the standard deviation of the contents is 81 milliliters. A new machine is tested on a sample of 24 containers and the standard deviation for this sample group is found to be 26 milliliters. At the 0.05 level of significance, test the claim that the amounts dispensed by the new machine have a smaller standard deviation.

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