Example 1:

A carnival ride is supposed to last at least five minutes.  Thirty-six operations of the ride are timed, and the following data (in second) were obtained.

Determine if there is sufficient evidence at the 0.05 level to conclude that the mean duration of the ride is less than 5 minutes.

Example 2:

A fish wholesaler has a catch of several thousand lobsters.  A prospective buyer selected 50 at random and obtained the following weights in ounces.

The prospective buyer will purchase the entire catch if it can be shown that the mean weight exceeds 19.9 ounces.  Formulate a suitable set of hypotheses, and conduct the test at the 1 percent significance level.

Example 3:

Is there relationship of IQ scores between twins?

Example 4:

Major physiological changes in body composition are a natural part of the aging process.  A physiologist wants to compare the mean body percent of water for 30-year-old males () with that of 60-year-old males ().  Random samples from the two age groups produced the following results.

Obtain a 95 percent confidence interval for () to estimate the difference in mean body percent of water for the 2 age groups.

Example 5:

An economist wanted to compare the hourly labor rates of automobile mechanics in two states.  Dealerships were randomly selected from each state, and the following hourly charges in dollars were obtained.

Test at the 0.05 significance level whether a difference exists in the mean hourly rates for these two states.  Assume that the sampled populations have the same standard deviation.

Example 6:

To determine if a new additive improves the mileage performance of gasoline, seven test runs were conducted with the additive, and six runs were made without it.  The test results appear below, with all figures in miles per gallon (mpg).

Is there sufficient evidence at the 0.05 level to conclude that the additive increases gasoline mileage?