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Problem 14 Easy Difficulty

In this section we showed how a simple random sample of 30 EAI managers can be used to develop point estimates of the population mean annual salary, the population standard deviation for annual salary, and the population proportion having completed the management training program.
a. Use Excel to select a simple random sample of 50 EAl managers.
b. Develop a point estimate of the mean annual salary.
c. Develop a point estimate of the population standard deviation for annual salary.
d. Develop a point estimate of the population proportion having completed the management training program.

Answer

a. There are 2500 managers given in the data list.
Select 2500 random numbers between 0 and 1, each number will correspond with one of the managers.
The sample will then consist of the 50 managers with the 50 smallest random numbers.
b. The point estimate of the mean anmual salary is the sample mean. The mean is the sum of all values divided by the number of values.
c. The point estimate for the population standard deviation for annual salary is the sample standard deviation. The variance is the sum of squared deviations from the mean divided by $n-1=50-1=49 .$ The standard deviation is the square root of the variance.
d. The point estimateof the population proportion is the sample proportion.
The sample proportion is the number of successes divided by the sample size of $50 .$

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Video Transcript

All right, So this question wants us to sample 50 Wrong. The total 2500 using Excel. So since everyone's answers, we're gonna be totally I'll just talk. Get this. So first, like, always will pull up our sampling procedure where first we label each element in the population between one and capital end. So in this case will have cells ranging from 1 to 2500. Then we'll give it random number between zero and one for each cell and then finally will pick the lowest 50 numbers to be our sample. Then Part B wants us to find an estimate for the population. Mean so we want a point estimate. So our point estimate is going to be X bar, which is the sample mean, which is just the sum of all the X values which our salaries someone well, the salaries divided by our sample size, which in this case is 50 managers, then part See, we want an estimate for our standard deviation. So we'll use SX, which is our sample standard deviation, which is equal to Since this is a sample, it's one over and minus one times the sum of each points distance from the mean squared. And then part D wants us to find a point estimate of the population proportion having completed the training program. So Rp hat is simply number of successes over total, which is in this case number yes, over 50.