According to the United States Census Bureau, the average single-family home constructed in 2016 was 2,431 square feet. Carmen wondered if families in her area still want a smaller home in comparison to the average. She randomly selected 67 people and asked what the ideal square footage of a home is for them. From the responses, she calculated the sample mean equals 1,390 square feet with a sample standard deviation of 65 square feet. Calculate the value of the test statistic.
A) -0.83
B) 1.82
C) -1.96
D) 0.83

Question

Quizplus · Accepted Answer

The test statistic is calculated using the formula $z = \frac{\bar{x} - \mu}{(\sigma / \sqrt{n})}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the sample standard deviation, and $n$ is the sample size. Plugging in the given values: $z = \frac{1390 - 2431}{(65 / \sqrt{67})}$, which results in a value close to -1.96, indicating option C is correct.

According to the United States Census Bureau, the Average Single-Family