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 cigarettes. do the cigarette filters appear to be effective? (hint: the filters reduce the amount of tar ingested by the smoker.) click the icon to view the frequency distributions (round to the nearest percent as needed.) do cigarette filters appear to be effective? a. no, because the relative frequency of the higher tar classes is greater for filtered cigarettes b. no, because the relative frequencies for each are not substantially different c. yes, because the relative frequency of the higher tar classes is greater for non - filtered cigarettes d. this cannot be determined

Explanation:

Step1: Calculate total frequency for non - filtered

For non - filtered cigarettes, total frequency $=2 + 0+14 + 7+2=25$.

Step2: Calculate relative frequencies for non - filtered

For $15 - 19$ mg: $\text{Relative Frequency}=\frac{2}{25}\times100\% = 8\%$.
For $20 - 24$ mg: $\text{Relative Frequency}=\frac{0}{25}\times100\% = 0\%$.
For $25 - 29$ mg: $\text{Relative Frequency}=\frac{14}{25}\times100\% = 56\%$.
For $30 - 34$ mg: $\text{Relative Frequency}=\frac{7}{25}\times100\% = 28\%$.
For $35 - 39$ mg: $\text{Relative Frequency}=\frac{2}{25}\times100\% = 8\%$.

Step3: Calculate total frequency for filtered

For filtered cigarettes, total frequency $=2 + 2+5 + 16=25$.

Step4: Calculate relative frequencies for filtered

For $5 - 9$ mg: $\text{Relative Frequency}=\frac{2}{25}\times100\% = 8\%$.
For $10 - 14$ mg: $\text{Relative Frequency}=\frac{2}{25}\times100\% = 8\%$.
For $15 - 19$ mg: $\text{Relative Frequency}=\frac{5}{25}\times100\% = 20\%$.
For $20 - 24$ mg: $\text{Relative Frequency}=\frac{16}{25}\times100\% = 64\%$.

Step5: Analyze effectiveness

The relative frequency of the higher tar classes ($25 - 39$ mg) is $28\%+8\% = 36\%$ for non - filtered and $0\%$ for filtered in the $25 - 39$ mg range. The relative frequency of the higher tar classes is greater for non - filtered cigarettes.

Answer:

Tar (mg)	Relative Frequency (Nonfiltered)	Relative Frequency (Filtered)
10 - 14	0%	8%
15 - 19	8%	20%
20 - 24	0%	64%
25 - 29	56%	0%
30 - 34	28%	0%
35 - 39	8%	0%

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