In 1930,the average size of a public restroom was 172 square feet;by 1990,due to federal disability laws,the average size had increased to 471 square feet.Suppose that a design team believes that this standard has increased from the 1990 level.They randomly sample 23 public restrooms in a major Midwestern city and obtain a mean square footage of 498.78 with a standard deviation of 46.94.Calculate the appropriate test statistic to test the hypotheses.
A)2.84
B)13.61
C)30.34
D)-2.84
E)-13.61

Question

Quizplus · Accepted Answer

The test statistic is calculated using the formula for a one-sample t-test: $ t = \frac{\bar{x} - \mu}{s/\sqrt{n}} $, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $s$ is the sample standard deviation, and $n$ is the sample size. Plugging in the values: $ t = \frac{498.78 - 471}{46.94/\sqrt{23}} \approx 2.84 $.

In 1930,the Average Size of a Public Restroom Was 172