You are a financial analyst for a brokerage firm. You want to compare dividend yields between stocks listed on the NYSE \& NASDAQ. You collect the following data:
$\begin{array}{lrr}\text { Number } & \text { NYSE } & \text { NASDAQ } \\ \text { Mean } & 31 & 25 \\ \text { Std dev } & 3.27 & 2.53 \\ 1.30 & 1.16\end{array}$
Is there a difference in the variances between the NYSE NASDAQ at the $\alpha=0.10$ level?
Answer
\(\boxed{\text{Final Answer:}}\) Since the F-statistic (1.67) is less than the critical value (9964709795.4) at the α=0.10 level, there is no significant difference in the variances between the NYSE and NASDAQ.
Step 1 ：Calculate the variances by squaring the standard deviations: \(variance_{NYSE} = 3.27^2 = 10.69\) and \(variance_{NASDAQ} = 2.53^2 = 6.40\)
Step 2 ：Calculate the F-statistic: \(F = \frac{variance_{NYSE}}{variance_{NASDAQ}} = \frac{10.69}{6.40} = 1.67\)
Step 3 ：Find the critical value from the F-distribution table or calculator for α=0.10 and degrees of freedom: \(critical\ value = 9964709795.4\)
Step 4 ：\(\boxed{\text{Final Answer:}}\) Since the F-statistic (1.67) is less than the critical value (9964709795.4) at the α=0.10 level, there is no significant difference in the variances between the NYSE and NASDAQ.
