The workers union at a certain university is quite strong. About 94% of all workers employed by the university belong to the workers union. Recently, the workers went on strike and now a local TV station plans to interview a sample of 20 workers ,chosen at random to get their opinions on the strike.
Estimate the number of workers in the sample who are union members by giving the mean of relevant distribution do not round
Quantify the uncertainty of your estimate by giving the standard deviation of distribution. Round ur response to the first 3 decimal places
Answer
To estimate the number of workers in the sample who are union members, we can use the concept of sampling distribution. Since 94% of all workers belong to the workers union, we can expect a similar proportion in our sample.
Mean of the relevant distribution:
The mean of the relevant distribution can be calculated by multiplying the proportion of workers who are union members by the total number of workers in the sample. In this case, we have 20 workers in the sample, so the mean is:
Mean = 20 * 0.94
Therefore, the mean of the relevant distribution is 18.8.
Standard deviation of the distribution:
To calculate the standard deviation, we need to use the formula for the standard deviation of a binomial distribution, which is the square root of n * p * (1 - p), where n is the sample size and p is the proportion of success (in this case, the proportion of workers who are union members).
Standard Deviation = sqrt(20 * 0.94 * (1 - 0.94))
Simplifying the equation gives:
Standard Deviation ≈ sqrt(20 * 0.94 * 0.06)
Therefore, the standard deviation of the distribution is approximately 1.323 (rounded to the first 3 decimal places).
In summary, the estimated number of workers in the sample who are union members is 18.8, and the standard deviation of the distribution is approximately 1.323.