# Variance of the population

Show your work!

All work must be done solely by you. Initial here as your signature that you received no outside help in the exam:

1. Given the following set of data (it is a population):

3, 20, 2, 12, 91, 12, 23, 12, 29, 19, 12, 39, 44, 37, 18, 29, 12, 27, 12

Using Excel’s embedded formulas and UPLOADING YOUR EXCEL SHEET, find the:

a. Mean

b. Median

c. Mode

d. Range

e. The variance of the population

f. The standard deviation of the population

g. The 80th percentile

h. The IQR (interquartile range)

i. Discuss whether or not an outlier exists in the data. Support your answer with mathematical evidence.

j. The probability of drawing a number higher than 22 if one number was drawn at random from the list

k. The probability of drawing a number higher than 22, not putting it back, and then drawing a second number higher than 22 from the list

l. The probability of drawing a number higher than 22 GIVEN THAT an even number was drawn.

Upload your Excel sheet to the final that you used for this. You must show the embedded formulas.

2. Create and insert a scatter diagram with a trendline in EXCEL for the following:

Book |
Pages (x variable) |
Price (y variable) |

A |
277 | $6.00 |

B |
477 | $7.25 |

C |
364 | $6.80 |

D |
411 | $6.50 |

E |
236 | $5.95 |

F |
284 | $5.99 |

G |
158 | $4.55 |

H |
515 | $8.00 |

Then

a. Show the equation of the trendline on the scatter diagram along with the coefficient of correlation (r squared).

b. Using Pearson’s Product Moment Correlation Coefficient, discuss the strength (strong, weak…) and type (positive, negative) of the relationship between pages and price. Make sure you have stated the value of r.

c. According to the trendline, how much should a book that is 560 pages cost?

d. According to the trendline, how many pages should a book that cost 9 dollars have?

3. Conduct a full hypothesis test using the p value method for the scenario below. Make sure all the steps are there. A good thing to do is to get the prompts from the Week 6 written assignment.

A sample of 12 account balances of a credit company showed a mean customer balance of $2,000, but the marketing manager claimed that the mean balance for the population was $2,300. The marketing manager did NOT have the population standard deviation, but the sample standard deviation was found to be $220. Use the p-value approach to conduct a full hypothesis test (all steps) that can be used to determine whether the mean of all account balances is significantly different from $2,300. Let α = .05.

4. Weekly demand at a grocery store for a brand of breakfast cereal is normally distributed with a mean of 600 boxes and standard deviation of 40 boxes.

Sketch and insert the z graph with appropriate labels and shading and then determine the probability that the weekly demand is:

a. 570 boxes or less.

b. More than 650 boxes.

c. Between 610 and 630 boxes.

5. In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 673 pieces of carry-on luggage was collected and weighed. The average weight was 28.9 pounds. Assume that we know the standard deviation of the population to be 3.94 pounds. Determine a 95% confidence interval estimate for the mean weight of the carry-on luggage.