Question

Identify Population Parameters From Sample Statistics Prompt: The owners of a small mail order business want to estimate their average annual sales. They randomly select 100 sales from their first quarter to analyze. For the samples, the average amount spent was $235.12 with a standard error of $12.41. Use what you have learned about sampling distributions to answer the following questions. Response Parameters What conditions, or assumptions, should be verified before using the sample values to estimate the population mean? If these conditions are satisfied, what is the probability that you would get a sample with a sample mean of $230.00 or less? If they expect to have 50,000 sales this year, what is their expected value of the total sales for the year? What do the following two values represent, in terms of the sampling distribution? *+ Zo 05 * = 5214.77 + 20.95 * = $255.47 What do these values mean in terms of the expected total sales for the year?

Answer 1

Solution:

first part:

• The sampled values must be independent of each other.

• Drawn Samples must be sampled randomly.

• The sample size must be sufficiently large, i,e he sample size, n should be no more than 10% of the population.

Second part:

Yes, Condition are satisfied

P(7 < 230) = P(Z = " < 230 – 235.12 12.42 Oi = P(Z < -0.41) = 0.3409 (use z table)

Third Part:

Expected Value=0.3409*50000= 17045

Fourth part:

it indicates 95% confidence interval of true mean,  that you can be 95% confident that the mean for the entire population of average sales in year is falls within $214.77 to $255.47 range