Question

# 6. (07.04 MC) Students at a local elementary school were randomly selected to participate in a...

6.

(07.04 MC)

Students at a local elementary school were randomly selected to participate in a reading fluency program. The program is designed to increase their reading fluency. A total of 17 students each took a pretest before the program and posttest after the program. The mean differences in the posttest and pretest is 11. The administration decided that all students in the school would participate in the program next school year. Let µA denote the mean score of the posttest and µB denote the mean score of the pretest for all students in the school. The 90 percent confidence interval estimate of the difference between the means for all students is (7, 15). What is an appropriate interpretation of the confidence interval? (4 points)

 For any µA and µB with (µA – µB) ≥ 9, the sample result is quite likely. µA is greater than µB, with a probability of 0.90. µA is less than µB, with a probability of 0.90. µA is approximately 15 and µB is approximately 7. For any µA and µB with 7 < (µA − µB) < 15, the sample result is quite likely.

8.

(07.02 LC)

A student working on a report about mathematicians decides to find the 98% confidence interval for the difference in mean age at the time of math discovery for Greek mathematicians versus Egyptian mathematicians. The student finds the ages at the time of math discovery for members of both groups, which include all Greek and Egyptian mathematicians, and uses a calculator to determine the 98% confidence interval based on the t distribution. Why is this procedure not appropriate in this context? (4 points)

 The sample sizes for the two groups are not equal. Age at the time of math discovery occurs at different intervals in the two countries, so the distribution of ages cannot be the same. Ages at the time of math discovery are likely to be skewed rather than bell shaped, so the assumptions for using this confidence interval formula are not valid. Age at the time of math discovery is likely to have a few large outliers, so the assumption for using this confidence interval formula is not valid. The entire population is measured in both cases, so the actual difference in means can be computed and a confidence interval should not be used.

9.

(07.02 LC)

The manager of a computer repair shop wants to compare the mean number of motherboard repairs in a week for two repair techniques. Twenty-four technicians from the shop are selected randomly, and each technician is assigned randomly to one of the two techniques. After teaching 12 technicians one technique and 12 technicians the other technique, the manager records the number of motherboard repairs each technician performs in one week. Which of the following is the MOST appropriate inferential statistical test in this situation? (5 points)

 A one-sample z-test A paired t-test A two-sample t-test A chi-square goodness-of-fit test A one-sample t-test

10.

(07.02 LC)

Randall is conducting a test on bacteria on slices of cheese. He uses 10 slices of cheese to compare two strains of bacteria. He applies one strain to the left side of the cheese and one strain to the right side. He flips a coin to decide which strain goes on the right side of the cheese. The bacteria holes that appear on each side are counted and he records them in a table.

Cheese Number of Holes for Strain 1 Number of Holes for Strain 2

1

25

19

2

21

15

3

13

14

4

13

12

5

14

10

6

12

9

7

11

5

8

11

5

9

8

4

10

5

4

If Randall is to perform an appropriate t-test to determine if there is a difference in the mean number of holes per slice of cheese produced by the two strains, how many degrees of freedom should he use? (4 points)

 7 8 9 10 18

11.

(07.05 MC)

In a study of the performance of a tires, the width of tires (in inches) and the life span (in months) for 14 tires were recorded. A regression line was a satisfactory description of the relationship between width of tire and tire life span. The results of the regression analysis are shown in the table.

Variable Coeff SE Coeff t Ratio p-Value
Constant 7.3985 0.5638 13.12 0.034
Width of tires 3.9571 0.7382 5.36 0.005

R squared = 88.5%

Which of the following should be used to compute a 98% confidence interval for the slope of the regression line? (5 points)

 7.3985 ± 2.681(0.5638) 7.3985 ± 2.624(0.5638) 3.9571 ± 2.65(0.7382) 3.9571 ± 2.624(0.7382) 3.9571 ± 2.681(0.7382)

12.

(07.05 LC)

The weight (in pounds) and the number of offspring of 23 randomly selected rabbits are compared. Which significance test should be used to determine whether a linear relationship exists between weight and number of offspring, provided the assumptions of the test are met? (4 points)

 A two-sample z-test A two-sample t-test A t-test for the slope of the regression line A chi-square test of independence A chi-square goodness-of-fit test

Solution7:

we are

The 90 percent confident that the true difference between the means for all students lies in between 7 and 15

For any µA and µB with 7 < (µA − µB) < 15, the sample result is quite likely

Solution9:

teaching 12 technicians one technique and 12 technicians the other technique, the manager records the number of motherboard repairs each technician performs in one week.

n1=12 ,n2=12

n1,n2 are independent samples

n1,n2<30

perform t test for difference in means

A two-sample t-test

Solution10:

df=n1+n2-2=10+10-2=18

18

Solution11:

slope-margin of errror,slope +margin of error

margin of error=Tc*sd/sqrt(n)

df=14-2=12

t crit==T.INV.2T(0.02;12)=2.680998=2.681

std error of slope=0.7382

hence MOE=0.7382*2.680998=1.979113

98% confidence interval for the slope of the regression line

slope-MOE,slope+MOE

slope=3.9571

correction option

3.9571 ± 2.681(0.7382)