Twenty volunteers at a cold research institute caught a cold after having been exposed to various cold viruses. Ten of the volunteers were randomly selected to receive tablets containing 1 gram of vitamin C. These tablets were taken four times a day. The control group, consisting of the other 10 volunteers, was given placebo tablets that looked and tasted exactly like the vitamin C ones. This was continued for each volunteer until a doctor, who did not know whether one volunteer was receiving vitamin C or the placebo, decided that the volunteer was no longer suffering from the cold. The length of time the cold lasted was then recorded. At the end of the experiment, the following data resulted:The average length of cold for the n 1 ==10 people treated with vitamin C is with a standard deviation of s 1 ==0.76 The average length of cold for the n 2 ==10 people receiving the placebo is with a standard deviation of s 2 =0.85 Determine the value of the pooled standard deviation . Round your answer three decimal places.

Question

Twenty volunteers at a cold research institute caught a cold after having been exposed to various cold viruses. Ten of the volunteers were randomly selected to receive tablets containing 1 gram of vitamin C. These tablets were taken four times a day. The control group, consisting of the other 10 volunteers, was given placebo tablets that looked and tasted exactly like the vitamin C ones. This was continued for each volunteer until a doctor, who did not know whether one volunteer was receiving vitamin C or the placebo, decided that the volunteer was no longer suffering from the cold. The length of time the cold lasted was then recorded. At the end of the experiment, the following data resulted:The average length of cold for the       n    1    ==10 people treated with vitamin C is with a standard deviation of       s    1    ==0.76 The average length of cold for the       n    2    ==10 people receiving the placebo is with a standard deviation of       s    2    =0.85 Determine the value of the pooled standard deviation . Round your answer three decimal places.

pawia6g · Accepted Answer

Solution:From the given information, n1=10, s1=0.76, n2=10 and s2=0.85.The pooled standard deviation is obtained by using the following formula:      S          p      o      o      l      e      d        =                    (                  n          1                −        1        )                  s          1          2                +        (                  n          2                −        1        )                  s          2          2                                      n          1                +                  n          2                −        2            Then,      S          p      o      o      l      e      d        =                    (                  n          1                −        1        )                  s          1          2                +        (                  n          2                −        1        )                  s          2          2                                      n          1                +                  n          2                −        2                =                    (        10        −        1        )                  0.76          2                +        (        10        −        1        )                  0.85          2                            10        +        10        −        2                =            11.7009      18          =  0.806Thus, the value of the pooled standard deviation is 0.806.

Answered question

Answer & Explanation

New Questions in College Statistics