Take home Test (80%)
1. (15pts) An engineer wanted to know whether the strength of two different concrete mix designs differed significantly. He randomly selected 9 cylinders, measuring 6 inches in diameter and 12 inches in height, into which mixture 301 was poured. After 28 days, he measured the strength of the cylinder. He also randomly selected 10 cylinders of mixture 400 and performed the same test. The results are as follow:
Mixture 301: 3960 4090 3100 3530 3200 3780 4080 4040 2940
Mixture 400: 4070 4890 5020 4330 4640 5220 4190 3730 4120 4620 Test the claim that mixture 400 is stronger than mixture 301 at the significant level in following steps.
a. (2 pts) Formulate null and alternative hypotheses:
b. (3 pts) Check assumptions
c. (8 pts) Compute the test statistics
d. (3 pts) Use P-value approach to make a decision.
2. (20 pts) The Centers for Disease Control and Prevention reported a survey of randomly selected Americans age 65 and older, which found that 411 of 1012 mean and 535 of 1062 women suffered from some form of arthritis.
a) (8 pts) Test the claim that
a different proportion
of senior men and women who have this disease at the α = 0.05.
b) (6 pts) Construct a 95% confidence interval for the difference in the proportions of senior mean and women who have this disease.
c) (3 pts) Interpret your interval in this context.
d) (3 pts) Does this confidence interval suggest that arthritis is more likely to afflict women than men? Explain.
Method 1
|
Method 2
|
Method 3
|
45
|
50
|
60
|
50
|
55
|
63
|
40
|
49
|
55
|
43
|
52
|
52
|
47
|
53
|
58
|
49
|
52
|
57
|
3. (25 pts) A director of training at a large temporary services company has learned of three different methods for teaching a person to type. He is interested in determining if there is a difference in average typing speed for employees who are taught to type by each of the three methods. He randomly selects 18 new employees and then randomly assigns six employees to learn to type by each of the typing methods. At the end of the course, he measures the number of correct words typed per minute for each employee. The results are as follows:
a. (2 pts) Write null hypothesis and alternative hypothesis.
H0: _____________________ , H1: ______________________________________________________.
b. (7 pts) Check the assumptions and find MST, MSE, and the test statistic of with degrees of freedom of numerator and denominator.
Check the assumptions:
, P-value =_______________________.
c. (2 point) Make a decision and draw a conclusion with level of significance
d. (12 pts) If the null hypothesis is rejected in part a, use Tukey’s test to determine which pairwise means differ using a familywise error rate of α = 0.05, where from the table of critical values for Tukey’s Test.
H0: __________________ versus H1: ____________________.
The test statistic
Decision:
H0: __________________ versus H1: ____________________.
The test statistic
Decision:
H0: __________________ versus H1: ____________________.
The test statistic
Decision:
e. (2 pts) Use lines to indicate which population means are not significantly different.
4. (20 pts) It is difficult to determine a person’s body fat percentage accurately without immersing him or her in water. Researchers hoping to find ways to make a good estimate immersed 20 male subjects, then measured their waist shown in the table.
A. (4 pts) Treating waist as the explanatory variable, x, determine the estimates of and .
B. Assuming the residuals are normally distributed, test whether a linear relation exists between waist and body fat in percentage at the level of significance.
· (2 pts)
· (2 pts) Comments on the assumptions:
a. The adequacy of the linear model: A plot of the residuals against the explanatory variable is ________________________
b. A constant error variance
c. is normal distributed
· ( 5 pts) Compute test statistic:
· (2 pts) Compute P-value:
C. (3 pts) Construct a confidence interval about the slope of the least-squares regression model
Lower bound=
upper bound=
D. (2 pts) What is the mean body fat percentage of people with waist of 42 inches? Can we use the least-squares regression line to find the mean body fat percentage with waist of 60 inches?