Problem
3. Do different grades of gasoline affect mileage? A test car made 5 trial runs with each of three different grades of gasoline. The resulting mileage is recorded in the table below. \begin{tabular}{|c|c|c|} \hline Regular & Premium & Super Premium \\ \hline 29 & 28 & 29 \\ \hline 30 & 31 & 29 \\ \hline 28 & 29 & 30 \\ \hline 30 & 32 & 33 \\ \hline 29 & 32 & 34 \\ \hline \end{tabular} I sample siz \[ \frac{\left(\Sigma x_{T O T}\right)^{2}}{N} \] \[ \begin{array}{l} \text { Test to determine if there is any difference in the population mean mileage with th } \\ \text { gasoline. Use a } 1 \% \text { significance level. } \\ H_{0}: \mu_{1}=\mu_{2}=M_{3} \text { at lecst } 2 \text { d } \end{array} \] \[ F=1.326 \quad \text { Fail to reject } H_{0} \text {, we are } 1 \% \] $F_{2}=6.93$ there is cosig dif in mileage with dif grades of gasoline. 4. At a local high school the freshman women's basketball team has a friendly rivalry with the women's varsity basketball team. They record and compare the number of points each team scores in every practice game. A random sample of 31 records for the freshman team shows a sample mean 63.2 points with a sample variance of 590.49 points $^{2}$. An independent random sample of 26 records from the varsity women's basketball team has a sample mean of 96. . points and a sample variance of 268.96 points ${ }^{2}$. Use the $5 \%$ level of significance to test the claim that the varsity team is more consistent in scoring than the freshman team. \[ H_{0}: \rho_{1}^{2}=\rho_{2}^{2} \quad F=4.820 \] \[ H_{1}: 0_{1}^{2}>0_{2}^{2} \]
Solution
Step 1 ：Calculate the F-statistic: \(F = \frac{590.49}{268.96} = 2.1955\)
Step 2 ：Calculate the p-value: p-value = 0.0241
Step 3 ：Compare p-value to significance level: 0.0241 < 0.05
Step 4 ：\boxed{\text{Reject the null hypothesis. The varsity team is more consistent in scoring than the freshman team.}}
