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.
\[
H_{0}: \rho_{1}^{2}=\rho_{2}^{2} \quad F=4.820
\]
\[
H_{1}: 0_{1}^{2}> 0_{2}^{2}
\]