Question

Indicted Governor. On Thursday, June 13, 1996, thenArizona Governor Fife Symington was indicted on $23$counts of fraud and extortion. Just hours after the federal prosecutors announced the indictment, several polls were conducted of Arizonans asking whether they thought Symington should resign. A poll conducted by Research Resources, Inc., that appeared in the Phoenix Gazette, revealed that $58\%$of Arizonans felt that Symington should resign; it had a margin of error of plus or minus $4.9$ percentage points. Another poll, conducted by Phoenix-based Behavior Research Center and appearing in the Tempe Daily News, reported that $54\%$ of Arizonans felt that Symington should resign; it had a margin of error of plus or minus $4.4$ percentage points. Can the conclusions of both polls be correct? Explain your answer.

Short answer

It's possible that the results of both polls are correct.

Step-by-step solution

Given Information

In a poll conducted by Research Resource Inc reported that $58\%$(with a margin of error of plus or minus $4.9\%$points of Arizonians felt that Governor Symington should resign.

In a second poll conducted by Behavior Research Center, reported that $54\%$(with a margin of error of plus or minus

$4.4\%$points of Arizonians felt that Governor Symington should resign.

Explanation

Assume that both surveys utilized a confidence level of $95\%$.

As a result, both polls give the percentage/proportion of Arizonians who believe Governor Symington should resign at a $95\%$confidence level.

According to the data, the Research Resource Inc poll's confidence interval ranges from $53.1\%$to $62.9\%$$(58\pm 4.9)$.

The Behavior Research Center's confidence interval is $49.6\%$ to $58.4\%$ $(54\pm 4.4)$.

It should be noticed that both surveys give common credible results ranging from $53.1\%$ to $58.4\%$.

As a result, it's feasible that the conclusions of both polls are right.