Please type your answer following each question and submit your work electronically to
CANVAS by the due date.
Please state clearly how you reach each answer. A numerical value is not a complete
answer. A question on hypothesis needs to have four basic parts: Part1: specifying the
null hypothesis and the alternative hypothesis; Part 2: identifying the sample information;
Part 3: Finding the p-value use the appropriate procedure; Part 4: Drawing the conclusion
by combining the sample information with the p-value in terms of the null hypothesis.
1. The times (in minutes) required by three workers to perform. an assembly-line task were
recorded on ten randomly selected occasions as follows.
Hank: 8, 10, 9, 11, 12, 15, 10, 8, 9, 11
Susan 12, 9, 16, 12, 10, 7, 10, 8, 9, 16
Joseph 9, 12, 5, 6, 7, 3, 5, 8, 5, 8
1.1) What are the factors that affect the assembly time among the three workers?
(between group variation)
1.2) What are the factors that may affect each person’s assembly time? (within group
variation)
1.3) What are the null and alternative hypotheses?
1.4) What are the assumptions?
1.5) Is it plausible to claim that the three workers have different mean assembly times at
0.05 significance level?
2. The U. S. Bureau of the Census collects data on monthly rents of newly completed
apartments and publishes the results in Current Housing Reports. Independent random
samples of monthly rents for newly completed apartments in the four U.S. regions yield the
following data, in dollars.
Northeast 905, 798, 1081, 1141, 1521
Midwest 870, 745, 699, 812, 702, 606, 519
South 912, 650, 883, 781, 1201, 1138
West 873, 783, 906, 877, 1108, 1302
2.1) Discuss the region effects on apartment renting.
2.2) What are the factors that affect the renting price within each region?
2.3) Use ANOVA to test the significance of the region effect on apartment renting at 0.01
significance level.
2.4) Simultaneously estimate the mean rent differences at 95% confidence level.
3. The following is a random sample of the sale prices of three types of Toyota Camry (L, LE,
and SE) in Chicago, Detroit, Boston and New York.
L L L LE LE LE SE SE SE
C h i c a g o 2 4 , 2 3 1 2 4 , 1 1 3 2 2 , 9 8 8 2 5 , 3 3 7 2 5 , 7 7 1 2 5 , 6 5 2 2 8 , 2 2 9 2 7 , 8 8 9 2 9 , 1 1 8
D e t r oi t 2 2 , 0 4 1 2 1 , 6 2 2 2 1 , 8 1 1 2 2 , 6 1 2 2 2 , 8 9 1 2 2 , 4 5 8 2 3 , 1 9 9 2 2 , 8 9 9 2 3 , 9 9 9
B os t on 2 3 , 1 6 7 2 4 , 1 1 4 23191 2 4 , 4 5 6 2 6 , 1 2 2 2 5 , 3 2 9 2 6 , 3 3 2 2 7 , 3 4 9 2 7 , 1 8 7
N e w Y or k 2 5 , 2 3 3 2 4 , 9 1 3 2 4 , 8 3 1 2 6 , 3 5 2 2 6 , 7 2 8 26355 2 9 , 1 2 9 2 8 , 7 2 9 2 9 , 8 1 6
3.1) Test whether there is any city effect on the car sale prices at 0.05 significance level
3.2) Test whether there is any type effect on the car sale prices at 0.05 significance level
3.3) Is there any interactions on car prices between location and the type of the car at 0.05
significance level?
3.4) Interpret the meaning of interaction term in 3.3).