Questions: Beity tabulated the miles-per-gallon values for her car as 26.5, 28, 30.2, 29.6, 32.3, and 24.7. The sample standard deviation is 2.728. The driver's manual for Betty's car lists the mpg for her car as 25. t = (x̄ - μ) / (s / √n) The test statistic for a two-sided test would be - 3.198 - 7.808 - 0.217 - 0.531

Solution Steps

To find the sample mean \( \bar{x} \) of the miles-per-gallon (mpg) values, we use the formula:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} \]

Substituting the values:

\[ \mu = \frac{171.3}{6} = 28.55 \]

The test statistic \( t \) is calculated using the formula:

\[ t = \frac{\bar{x} - \mu}{s / \sqrt{n}} \]

Where:

• \( \bar{x} = 28.55 \) (sample mean)
• \( \mu = 25 \) (hypothesized population mean)
• \( s = 2.728 \) (sample standard deviation)
• \( n = 6 \) (sample size)

Substituting the values:

\[ t = \frac{28.55 - 25}{2.728 / \sqrt{6}} \approx 3.188 \]

Final Answer