For the data in Textbook Problem $21\mathrm{.}40,$ summary statistics from SAS are given below

Do the data analysis using the following steps:

$($a$)$ Conduct an $F$ test to check if the two populations can be assumed to have equal variances:$21\mathrm{.}40$ The Power of Positive Thinking? Does the way the press depicts the economic future affect

the stock market? To investigate this, researchers analyzed the longest article about economic

conditions from the front page of the Money section of USA Today from a randomly chosen

weekday of each week between August $2007$ and June $2009.$ Articles were rated as to how positive or

negative they were about the economic future. For each week, the change in the Dow Jones

Industrial Average $($average DJIA value the week after the article appeared minus the average the

week the article appeared$)$ was computed. Positive values of the change indicate that the DJIA

increased. $)22$

Here are the changes in DJIA values corresponding to very negative articles:

Is there good evidence that the DJIA performs differently after very positive articles than after very

negative articles?