math

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math 210 quizes

1. The graph of a linear inequality consists of a line and some points on both sides of the line.

Answer

True False

Question 2

When the constraints of a Linear Programming problem have ≤ signs, then you are finding the maximum value of the profit.

Answer True False

Question 3

The graph of a linear inequality consists of a line and all of the points on one side of the line.

Answer True False

Question 4

If a linear programming problem has a solution at all, it will have a solution at some corner of the feasible set.

Answer True False

Question 5

No point other than a corner of the feasible set can be a solution to a Linear Programming problem.

Answer True False

Question 6

No point in the interior of the feasible set can be a solution to a Linear Programming problem.

Answer True False

Question 7

Every Linear Programming problem with a bounded nonempty feasible region has a solution.

Answer True False

Question 8

No linear Programming problem with an unbounded feasible region has a solution.

Answer True False

Question 9

The graphical method is the only practical method for all Linear Programming problems.

Answer True False

Question 10

In a feasible basic solution all the variables (with the possible exception of the objective) are nonnegative.

Answer True False

math 216 quizes

Question 1

The following null hypothesis has been formulated to test for the equality of three population means: H0: u1 = u2 = u3. Choose the correct alternative hypothesis. Hint: Refer to One-Way ANOVA Test p. 536 in OCR.

Answer

A. u1 > u2 > u3

B. Not all the means are equal.

C. u1 < u2 < u3

D. u1 = u2 < u3

2 points

Question 2

Four machines were compared with respect to the mean length of a common product that they produce. Random samples of 5 units each were selected from the machines’ production lines. When the test for equal means was performed, it was reported that the P-value was 0.025 < P < 0.05. What are the bounds for the test statistic? Hint: Determine degrees of freedom, df (p. 538 in OCR) and then refer to Table VI.

Answer

A. 3.24 < test statistic < 4.08

B. test statistic > 5.29

C. 4.08 < test statistic < 4.29

D. test statistic < 3.24

Question 3

The standard deviations of 4 samples, each of size 10, were s1 = 2.4, s2 = 2.8, s3 = 3.0, s4 = 2.5. Which of the following is the correct value for the sum of squares within the groups? Hint: The sum of squares within each group is also called the error sum of squares or SSE. To calculate it, refer to formula on p. 529 and 531 of OCR)

Answer

A. 259.65

B. 28.85

C. 7.21

D. 96.30

Question 4

Three different methods were compared for reducing blood pressure in hypertensive patients. The reductions for the three methods was as follows: What is the sum of squares between the groups? Hint: The sum of squares between groups, SSTR, is also called the treatment sum of squares. The mean of each group needs to be calculated and then the overall mean needs to be calculated. These are used in the formula. Formula is on p. 529 and 531 of OCR.

Method 1 Method 2 Method 3

16 10 20

14 10 20

10 12 18

8 14 14

Answer

A. 52.33

B. 75.00

C. 104.67

D. 8.33

Question 5

Three different methods were compared for reducing blood pressure in hypertensive patients. The reductions for the three methods was as follows: What is the F statistic? Hint: The F-statistic takes several calculations. See p. 529 and 531 in the OCR. You may wish to use Excel for ANOVA in Course Materials Week 7 to find the F-statistic.

Method 1 Method 2 Method 3
16 10 20
14 10 20
10 12 18
8 14 14
Answer

A. 6.28

B. 7.68

C. 1.40

D. 2.33

week 6

12.38 Identify the type of table that is used to group bivariate data.

12.39 What are the small boxes inside the heavy lines of a con- tingency table called?

12.40 Suppose that bivariate data are to be grouped into a contin- gency table. Determine the number of cells that the contingency table will have if the number of possible values for the two vari- ables are

a. two and three.

b. four and three.

c. m and n.

12.41 Identify three ways in which the total number of observa- tions of bivariate data can be obtained from the frequencies in a contingency table.

week 9

14.3 Fill in the blanks.

a. The line y = β 0 + β 1 x is called the .

b. The common conditional standard deviation of the response variable is denoted .

c. For x = 6, the conditional distribution of the response vari- able is a distribution having mean and standard deviation .

14.4 What statistic is used to estimate

a. the y-intercept of the population regression line?

b. the slope of the population regression line?

c. the common conditional standard deviation, σ , of the response variable?

week 5

The American Freshman. In 2000, 27.7% of incoming freshmen characterized their political views as liberal, 51.9% as moderate, and 20.4% as conservative. For this year, a random sample of 500 incoming college freshmen yielded the preceding frequency distribution for political views.

a. Identify the population and variable under consideration here.

b. At the 5% significance level, do the data provide sufficient evidence to conclude that this year’s distribution of political views for incoming college freshmen has changed from the 2000 distribution?

c. Repeat part (b), using a significance level of 10%.

week 4

10.53 A Better Golf Tee? An independent golf equipment testing facility compared the difference in the performance of golf balls hit off a regular 2-3/4 ′′ wooden tee to those hit off a 3 ′′ Stinger Competition golf tee. A Callaway Great Big Bertha driver with 10 degrees of loft was used for the test, and a robot swung the club head at approximately 95 miles per hour. Data on total distance traveled (in yards) with each type of tee, based on the test results, are provided on the WeissStats CD.

a. Obtain normal probability plots, boxplots, and the standard deviations for the two samples.

b. At the 1% significance level, do the data provide sufficient ev- idence to conclude that, on average, the Stinger tee improves total distance traveled?

c. Find a 99% confidence interval for the difference between the mean total distance traveled with the regular and Stinger tees.

d. Are your procedures in parts (b) and (c) justified? Why or why not?