This week will require that you create a random sample in Excel, perform calcula

Question

This week will require that you create a random sample in Excel, perform calculations from that sample, and then interpret the results in a short paragraph. Using the Applewood Auto Group 2011 sales data (which is a population for the whole year), select a sample of 30 purchases, and calculate the sample mean of the buyers' ages. Then determine the population mean of buyers' ages and the population standard deviation of buyers' ages. Use this information to determine the likelihood of observing a sample mean as extreme or more extreme than the mean you found. (That is: as high or higher, as low or lower.) Write a short paragraph explaining your results and what they mean.

C Age of buyer Profit Location Vehicle-Type Previous purchases 43 $2,348 Tionesta Sedan 0 47 $3,292 Olean Sedan 2 43 $1,500 Tionesta Sedan 0 57 $2,279 Sheffield Hybrid 1 53 $1,401 Tionesta Sedan 2 52 $2,199 Tionesta SUV 0 45 $1,741 Olean Compact 2 37 $732 Olean SUV 1 49 $2,084 Tionesta Sedan 0 72 $1,640 Olean Sedan 1 47 $1,461 Kane Sedan 0 46 $1,238 Sheffield Compact 1 41 $1,876 Kane Sedan 2 33 $1,428 Kane SUV 2 54 $2,666 Tionesta Truck 0 31 $2,415 Kane Sedan 0 41 $2,165 Tionesta SUV 0 27 $1,529 Sheffield Sedan 1 42 $1,410 Kane SUV 2 42 $1,648 Olean SUV 0 30 $754 Olean Sedan 2 40 $1,509 Kane SUV 2 72 $1,821 Tionesta SUV 1 55 $2,989 Tionesta Compact 1 44 $1,897 Sheffield Compact 0 42 $1,298 Tionesta Sedan 1 40 $1,144 Tionesta Truck 0 51 $2,056 Sheffield Hybrid 0 48 $1,344 Sheffield SUV 0 53 $2,175 Olean Sedan 1 40 $1,638 Sheffield Sedan 0 49 $1,606 Olean Compact 0 46 $1,907 Olean Sedan 0 25 $1,040 Sheffield Compact 0 45 $820 Kane Compact 1 43 $2,498 Tionesta SUV 1 68 $1,837 Sheffield Sedan 1 47 $1,731 Tionesta Compact 0 21 $1,387 Tionesta Sedan 0 49 $1,827 Tionesta Truck 3 49 $1,915 Tionesta SUV 1 42 $2,071 Kane SUV 0 49 $1,680 Kane SUV 3 39 $996 Kane Compact 2 31 $1,809 Tionesta Sedan 1 31 $1,412 Sheffield Sedan 1 53 $1,220 Olean Sedan 0 61 $1,973 Kane SUV 3 58 $1,501 Sheffield Hybrid 1 48 $1,952 Tionesta Compact 1 41 $1,704 Sheffield Sedan 1 54 $2,584 Olean Compact 2 44 $2,886 Olean SUV 1 29 $1,342 Kane Sedan 2 51 $1,807 Tionesta Sedan 1 23 $1,754 Sheffield SUV 1 32 $2,207 Sheffield Compact 0

Explanation / Answer

From this 30 samples we calculate sample mean xbar as,

xbar = sum(xi) / n = 1363 / 30 = 45.4333

Now consider whole population N = 57 and we have to calculate population mean and population standard deviation as,

Population mean = sum(xi) / N = 2545 /57 = 44.6491

Population Standard deviation = sqrt((1/N-1)* sum(xi - Population mean)^2)

= sqrt((1/56)*6674.982

= 1 0.9177

Population Standard deviation = 10.9177

The sample mean is 45.4333 and population mean is 44.6491

The accuracy of population mean is comparatively higher than accuracy of the sample mean. the accuracy of the sample mean can be increased by increasing number of observations in the sample.sample mean is unbiased estimate of the population mean. As we increase the number of samples in the estimate of sample mean then bias goes on decreasing and we get more accurate result.Therefore likelihood of observing sample mean is as extrme than the population mean which can be overcome by increasing the samples in the estimate of the sample mean.

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