Week 8 – Final Exam
38637Final Exam
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: (5 point deduction if there are no initials)
1. Given the following set of data (it is a population):
12, 12, 16, 14, 12, 12, 16, 12, 19, 12, 12, 18, 28, 12, 27, 16, 161
Using Excel’s embedded formulas and UPLOADING YOUR EXCEL SHEET (10 point deduction if there is no uploaded sheet) with embedded calculations to demonstrate your skill at using computer technology for statistical analysis in a business setting, find the:
a. Mean
b. Median
c. Mode
d. Range
e. Variance of the population
f. Standard deviation of the population
g. The 40th percentile – inclusive
h. The IQR (interquartile range)
i. Discuss whether or not an outlier exists in the data. Support your answer with mathematical evidence and a formula.
j. The probability of drawing a number higher than 15 if one number was drawn at random from the list
k. The probability of drawing a number higher than 15, not putting it back, and then drawing a second number higher than 15 from the list
l. The probability of drawing a number higher than 15 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 trendline in EXCEL for the following:
Book Pages (x variable) Price (y variable)
A 175 $7.00
B 380 $9.25
C 215 $8.25
D 280 $8.75
E 190 $7.25
F 200 $7.50
G 150 $6.00
H 422 $9.99
Then
a. Show the equation of the trendline on the scatter diagram along with the coefficient of correlation (r squared). Upload your Excel sheet.
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 500 pages cost?
d. According to the trendline, how many pages should a book that cost 9 dollars have?
e. Discuss how confident you are in the answers to c and d, and use statistical concepts learned in this class to justify your answer.
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 119 account balances of a credit company showed a mean customer balance of $4,159, but the marketing manager claimed that the mean balance for the population was $4,200. The marketing manager said the population standard deviation was $92. 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 different from $4,200. Let α = .05.
4. Weekly demand at a grocery store for a brand of breakfast cereal is normally distributed with a mean of 400 boxes and standard deviation of 30 boxes.
Sketch and insert the z graph with appropriate labels and shading and then determine the probability that the weekly demand is:
a. 430 boxes or less.
b. More than 450 boxes.
c. Between 367 and 420 boxes.
5. In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 90 pieces of carry-on luggage was collected and weighed. The average weight was 24.6 pounds. Assume that we know the standard deviation of the population to be 7 pounds. Determine a 99% confidence interval estimate for the mean weight of the carry-on luggage.
6. True or False?
a. A sample is a subset of a population.
b. In a binomial experiment, there are only two outcomes.
c. As the confidence level increases for a data set, the range of the confidence interval decreases.
d. If you are finding a confidence interval for a mean, the mean will be in the center of your interval.
e. A trendline is the line of best fit for a data set.
f. The mean will always be the best representation of a set of data.
g. An outlier will affect a mode.
h. The area under a normal curve is 1.
i. If you were looking at a normal curve, the mean and median are found at the highest point of that curve.
j. When you have a large sample size and know the population standard deviation, then you use t instead of z.
k. A z value is a standard deviation and not a probability.
l. Conditional probability is used when you want to find the probability of one event happening after another, and the first event has already happened.
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