Question

construct one table that includes relative frequencies based on the frequency distributions shown below, then compare the amounts of tar in non - filtered and filtered (the amount of tar ingested by the smoker.) click the icon to view the frequency distributio complete the following relative frequency table. (round to the nearest percent as needed.) frequency (non - filtered) relative frequency (filtered) tar (mg) relative frequency tar (mg) 3 - 8 9 - 14 15 - 20 21 - 26 27 - 32 33 - 38 39 - 44 do cigarette filters appear to be effective? a. yes, because the relative frequency of the higher tar classes is greater for non - filtered cigarettes. b. no, because the relative frequency of the higher tar classes is greater for filtered cigarettes. c. no, because the relative frequencies for each are not substantially different. d. this cannot be determined.

Explanation:

Step1: Calculate total frequencies

For non - filtered: $2 + 1+13 + 7+2=25$. For filtered: $1 + 2+5 + 17=25$.

Step2: Calculate relative frequencies for non - filtered

For $3 - 8$ mg: $\frac{2}{25}\times100\% = 8\%$. For $9 - 14$ mg: $\frac{1}{25}\times100\% = 4\%$. For $15 - 20$ mg: $\frac{13}{25}\times100\% = 52\%$. For $21 - 26$ mg: $\frac{7}{25}\times100\% = 28\%$. For $33 - 38$ mg: $\frac{2}{25}\times100\% = 8\%$.

Step3: Calculate relative frequencies for filtered

For $3 - 8$ mg: $\frac{1}{25}\times100\% = 4\%$. For $9 - 14$ mg: $\frac{2}{25}\times100\% = 8\%$. For $15 - 20$ mg: $\frac{5}{25}\times100\% = 20\%$. For $21 - 26$ mg: $\frac{17}{25}\times100\% = 68\%$.

Step4: Analyze effectiveness of filters

The relative frequency of higher tar classes ($21 - 26$ mg and above) is greater for non - filtered cigarettes.

Answer:

Tar (mg)	Relative Frequency (Nonfiltered)	Relative Frequency (Filtered)
$9 - 14$	$4\%$	$8\%$
$15 - 20$	$52\%$	$20\%$
$21 - 26$	$28\%$	$68\%$
$33 - 38$	$8\%$	$0\%$
$39 - 44$	$0\%$	$0\%$

A. Yes, because the relative frequency of the higher tar classes is greater for nonfiltered cigarettes.