PSTAT 109: Lab 6 complete solutions correct answers key

PSTAT 109: Lab 6 complete solutions correct answers key

Fall 2015

Instructions: When you _nish all problems, ask your TA to check your work.

Problem 1 (Comparing random samples and populations). Open the Excel _le EAI.xlsx.

The data show the annual salary for all 2; 500 managers in one company.

a. What is the population mean annual salary?

b. What is the population standard deviation for annual salary?

Now, we want to construct 10 random samples each of size 25. One way to do this is as

follows:

(i) Assign a random number to each salary, so in the column adjacent to the salary

column, use the RAND function generate a list of random numbers uniformly dis-

tributed between 0 and 1.

(ii) Sort salaries by their corresponding random number. This can be accom-

plished by using the sort feature found in the Data tab. Sort by either ascending

or descending.

(iii) Take the _rst 25 sorted salaries as our _rst random sample. Copy and paste the

values of these 25 salaries into a new column.

(iv) Press F9. This will reassign a new random number to each salary.

(v) Repeat steps (ii), (iii), and (iv) until you have 10 random samples of size 25.

For each of the 10 random samples,

c. Find a point estimate of the population mean annual salary. (Consider using the

_ll-handle here.)

d. Find a point estimate of the population standard deviation. (Consider using the _ll-

handle here.)

e. How do the 10 point estimates of the population mean compare to the actual popula-

tion mean?

f. How do the 10 point estimates of the population standard deviation compare to the

actual population standard deviation.

Problem 2. Open the Excel _le GolfIncome.xlsx. The data represent income (in thou-

sands of dollars) earned by a population of 40 professional golfers from their endorsement

deals.

a. What is the probability that a golfer earned between 4; 000 and 6; 000 thousand dollars?

Hint: One way to _nd the number of incomes between 4; 000 and 6; 000 thousand

dollars is to use the COUNTIFS function.

b. How much did a golfer have to earn to be in the top 25% of the income bracket? Hint:

Sort ascending the dataset, then _nd the (100 􀀀 25) = 75th percentile (Recall the

percentile formula back in lecture 2).

Now, assume that the data follow a normal distribution. Using the NORM.DIST and NORM.INV

functions, determine the following:

c. What is the probability that a golfer earned between 4; 000 and 6; 000 thousand dollars?

d. How much did a golfer have to earn to be in the top 25% of the income bracket?