Lester Hollar is vice president for human resources for a large manufacturing company. In recent years, he has noticed an increase in absenteeism, which he thinks is related to the general health of the employees. Four years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each was absent in the six months before the exercise program began and in the last six months. Below are the results. Employee

Before

After

1

7
7

2

7
1

3

2
6

4

5
4

5

7
3

6

6
3

7

4
1

8

1

4

At the .05 significance level, can he conclude that the number of absences has declined? Estimate the p-value.
a. State the decision rule for 0.1 significance level: H0 : μd ≤ 0; H1 : μd > 0. (Round the final answer to 3 decimal places.)
Reject H0 if t > .
b. Compute the value of the test statistic. (Round the final answer to 3 decimal places.)
Value of the test statistic
c. Estimate the p-value? (Round the final answer to 4 decimal places.)
d. What is your decision regarding H0?
At the 0.05 significance level, (Click to select)do not rejectreject H0.

Successful implementation of a new system is based on three independent modules. module 1 works properly with probability 0.96. for modules 2 and 3, these probabilities equal 0.95 and 0.90. compute the probability that at least one of these three modules fails to work properly.

What numbers are included in the set of integers? what numbers are not included?

In δabc shown below, ∠bac is congruent to ∠bca: triangle abc, where angles a and c are congruent given: base ∠bac and ∠acb are congruent. prove: δabc is an isosceles triangle. when completed (fill in the blanks), the following paragraph proves that line segment ab is congruent to line segment bc making δabc an isosceles triangle. (4 points) construct a perpendicular bisector from point b to line segment ac . label the point of intersection between this perpendicular bisector and line segment ac as point d: m∠bda and m∠bdc is 90° by the definition of a perpendicular bisector. ∠bda is congruent to ∠bdc by the definition of congruent angles. line segment ad is congruent to line segment dc by by the definition of a perpendicular bisector. δbad is congruent to δbcd by the line segment ab is congruent to line segment bc because consequently, δabc is isosceles by definition of an isosceles triangle. 1. corresponding parts of congruent triangles are congruent (cpctc) 2. the definition of a perpendicular bisector 1. the definition of a perpendicular bisector 2. the definition of congruent angles 1. the definition of congruent angles 2. the definition of a perpendicular bisector 1. angle-side-angle (asa) postulate 2. corresponding parts of congruent triangles are congruent (cpctc)