Question

5 select the correct answer. when evaluating a survey, jody saw that 54% of the respondents think that the minimum age of those awarded a drivers license should be raised, while 46% think it should remain the same. the margin of error was ±5%. which statement is true? a. the population proportion of those who think the driving age should be raised is definitely greater than the proportion who think it should remain the same. b. the population proportion of those who think the driving age should be raised is definitely less than the proportion who think it should remain the same. c. the population proportion of those who think the driving age should be raised may or may not be greater than the proportion who think it should remain the same. d. the population proportion of those who think the driving age should be raised is definitely equal to the proportion who think it should remain the same.

Explanation:

Step1: Calculate confidence intervals

The proportion of those who think the driving - age should be raised is $54\%$ with a margin of error of $\pm5\%$. So the confidence interval is $49\%\leq p_{1}\leq59\%$. The proportion of those who think it should remain the same is $46\%$ with a margin of error of $\pm5\%$. So the confidence interval is $41\%\leq p_{2}\leq51\%$.

Step2: Analyze overlap of intervals

Since the confidence intervals overlap (the intervals $[49\%,59\%]$ and $[41\%,51\%]$ have an overlap), we cannot be certain that one proportion is greater than the other.

Answer:

C. The population proportion of those who think the driving age should be raised may or may not be greater than the proportion who think it should remain the same.