Studies are often done by pharmaceutical companies to determine the effectiveness of a treatment program. Suppose that a new AIDS antibody drug is currently under study. It is given to patients once the AIDS symptoms have revealed themselves. Of interest is the average (mean) length of time in months patients live once starting the treatment. Two researchers each follow a different set of 40 AIDS patients from the start of treatment until their deaths. The following data (in months) are collected.Researcher A: 3; 4; 11; 15; 16; 17; 22; 44; 37; 16; 14; 24; 25; 15; 26; 27; 33; 29; 35; 44; 13; 21; 22; 10; 12; 8; 40; 32; 26; 27; 31; 34; 29; 17; 8; 24; 18; 47; 33; 34Researcher B: 3; 14; 11; 5; 16; 17; 28; 41; 31; 18; 14; 14; 26; 25; 21; 22; 31; 2; 35; 44; 23; 21; 21; 16; 12; 18; 41; 22; 16; 25; 33; 34; 29; 13; 18; 24; 23; 42; 33; 29Complete the tables using the data provided. (Enter exact numbers as integers, fractions, or decimals.)Researcher ASurvival Length(in months) Frequency RelativeFrequency Cumulative RelativeFrequency0.5-6.5 6.5-12.5 12.5-18.5 18.5-24.5 24.5-30.5 30.5-36.5 36.5-42.5 42.5-48.5 Researcher BSurvival Length(in months) Frequency RelativeFrequency Cumulative RelativeFrequency0.5-6.5 6.5-12.5 12.5-18.5 18.5-24.5 24.5-30.5 30.5-36.5 36.5-45.5
Question
Studies are often done by pharmaceutical companies to determine the effectiveness of a treatment program. Suppose that a new AIDS antibody drug is currently under study. It is given to patients once the AIDS symptoms have revealed themselves. Of interest is the average (mean) length of time in months patients live once starting the treatment. Two researchers each follow a different set of 40 AIDS patients from the start of treatment until their deaths. The following data (in months) are collected.Researcher A: 3; 4; 11; 15; 16; 17; 22; 44; 37; 16; 14; 24; 25; 15; 26; 27; 33; 29; 35; 44; 13; 21; 22; 10; 12; 8; 40; 32; 26; 27; 31; 34; 29; 17; 8; 24; 18; 47; 33; 34Researcher B: 3; 14; 11; 5; 16; 17; 28; 41; 31; 18; 14; 14; 26; 25; 21; 22; 31; 2; 35; 44; 23; 21; 21; 16; 12; 18; 41; 22; 16; 25; 33; 34; 29; 13; 18; 24; 23; 42; 33; 29Complete the tables using the data provided. (Enter exact numbers as integers, fractions, or decimals.)Researcher ASurvival Length(in months) Frequency RelativeFrequency Cumulative RelativeFrequency0.5-6.5 6.5-12.5 12.5-18.5 18.5-24.5 24.5-30.5 30.5-36.5 36.5-42.5 42.5-48.5 Researcher BSurvival Length(in months) Frequency RelativeFrequency Cumulative RelativeFrequency0.5-6.5 6.5-12.5 12.5-18.5 18.5-24.5 24.5-30.5 30.5-36.5 36.5-45.5
Solution
To complete the tables, we first need to count the number of patients (frequency) that fall into each survival length category for both researchers. Then, we calculate the relative frequency by dividing the frequency by the total number of patients (40). The cumulative relative frequency is the sum of the relative frequencies up to that point.
Researcher A:
| Survival Length (in months) | Frequency | Relative Frequency | Cumulative Relative Frequency |
|---|---|---|---|
| 0.5-6.5 | 4 | 0.10 | 0.10 |
| 6.5-12.5 | 5 | 0.125 | 0.225 |
| 12.5-18.5 | 7 | 0.175 | 0.40 |
| 18.5-24.5 | 4 | 0.10 | 0.50 |
| 24.5-30.5 | 5 | 0.125 | 0.625 |
| 30.5-36.5 | 4 | 0.10 | 0.725 |
| 36.5-42.5 | 3 | 0.075 | 0.80 |
| 42.5-48.5 | 8 | 0.20 | 1.00 |
Researcher B:
| Survival Length (in months) | Frequency | Relative Frequency | Cumulative Relative Frequency |
|---|---|---|---|
| 0.5-6.5 | 3 | 0.075 | 0.075 |
| 6.5-12.5 | 4 | 0.10 | 0.175 |
| 12.5-18.5 | 8 | 0.20 | 0.375 |
| 18.5-24.5 | 6 | 0.15 | 0.525 |
| 24.5-30.5 | 4 | 0.10 | 0.625 |
| 30.5-36.5 | 5 | 0.125 | 0.75 |
| 36.5-42.5 | 5 | 0.125 | 0.875 |
| 42.5-48.5 | 5 | 0.125 | 1.00 |
Please note that the frequencies were calculated based on the provided data and the specified survival length intervals. The relative frequencies were calculated by dividing the frequency by the total number of patients (40). The cumulative relative frequencies were calculated by adding up the relative frequencies up to that point.
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