CALCULATIONS (40 Points)

Background Information

After graduation, you obtained a position as an Industrial/Organizational Psychologist to examine the productivity and job satisfaction of agents in a national real estate firm.A year ago, hundreds of real estate managers were EACH randomly assigned 16 recent real estate graduates from across the country.After a year of training,eachmanager'steam,made up of16 recent real estate graduates,reported their average salesof homes for the previous month.The entire population ofINDIVIDUALrecent real estate graduateshad anaverage monthly sale offifty properties(=50) witha standard deviation of eight properties(=8).

Dr. Che Amazu'snationalteam of (n=16) real estate agents had an averagemonthly saleof (M=53.78).What is the probability(as a percentage)thatother teams sold more homes thanDr.Amazu'sTEAM?Complete Parts 1, 2, and3below,showing ALL requiredformulas, calculations,and written/graphicwork.

Part1.Visualize the problem

On the figure below, drawa line that separates the distribution into two partsusing the z-score value of your sample.Identify (i.e., label) the area you are asked to calculatein the question above,aseitherBody or Tail.

If you want to complete entirely digitally (without printing, then scanning, uploading), you can move the orange box-and-arrowwith the z below,tolocate your sample in the distribution of sample means andsplit the graph in two parts.In orange box-and-arrow, be sure to replace the ### signs with theactualz-score for the sample, when you complete Part2.Thendrageithertheblue (Body) or purple (Tail) box-and-arrowover the distribution of sample means curvebelow,toidentifythe area you are asked to calculate as eitherBody or Tail.

[Hint: Use your unit normal table to becertain of your answers.](5 Points)

Part2.Calculate the Percentage

Then,calculateprobability(as a percentage)for the areadiscussed above.Be sure toalsowrite thepercentage valuein the areaaboveorlabel it with abox-and-arrow (15Points)

Part 3.Calculate a Confidence Interval

Letus assumethatyouDID NOTknow the true population mean was =50. The only information you had was the mean ofDr.Amazu's team (M=53.78). Now you want to compute a range of X scores that might include the value of the population mean.

1. Provide range ofX valuesthat capture95%of the scores about/aroundtheMeanofDr.Amazu's sample. (Hint:First, think about the steps, tables, and formula's you will need.)

1. Drag and drop the two box-and-arrows tocorrectlyindicate the upper and lower limits of the confidence interval you calculated.Be sure to insert the correct values into the box-and-arrow objects.(15Points)

LowerLimit=Mz(

M

)=()==

UpperLimit=M+z(

M

)=+()=+=

1. Does the true population mean of=50 fall within this range?Check the box forYESorNO(2Points)

1. Answer one of the following:(3Points)

• What can we inferaboutwhichpopulation Dr. Amazu samplecame from,ifpopulation mean of =50,ISFOUNDin the confidence intervalyou computed?Explainin a sentence or two.

OR

• What can we infer about which population Dr. Amazu sample came from,if population mean of =50,ISNOTFOUNDin the confidence intervalyou computed?Explainin a sentence or two.

Write response to Question d, here: