MA260 Lesson 8 Esam SCORE 95 PERCENT

Question 1

5 / 5 points

The following data were analyzed using one-way analysis of variance.
 

A

B

C

34

27

19

26

23

31

31

29

22

28

21

22


 
Which one of the following statements is correct?

Question options:

a) 

The purpose of the analysis is to determine whether the groups A, B, and C are independent.

b) 

The purpose of the analysis is to test the hypothesis that the population means of the three groups are equal.

c) 

The purpose of the analysis is to test the hypothesis that the population variances of the three groups are equal.

d) 

The purpose of the analysis is to test the hypothesis that the sample means of the three groups are equal.

Question 2

5 / 5 points

A golfer wished to find a ball that would travel more than 170 yards when hit with his 6-iron with a club head speed of 90 miles per hour. He had a golf equipment lab test a low-compression ball by having a robot swing his club 12 times at the required speed. State the null and alternative hypotheses for this test.

Question options:

a) 

H0:  µ > 170; Ha:  µ = 170

b) 

H0:  µ < 170; Ha:  µ = 170

c) 

H0:  µ = 170; Ha:  µ > 170

d) 

H0:  µ = 160; Ha:  µ > 160

Question 3

5 / 5 points

State the null and alternative hypothesis for the test associated with testing whether colorblindness and gender are dependent characteristics.

Question options:

a) 

H0:  Colorblindness and gender are dependent characteristics.
    Ha:  Colorblindness and gender aren't related in any way.

b) 

H0:  Colorblindness and gender are dependent characteristics.
    Ha:  Colorblindness and gender are related in some way.

c) 

H0:  Colorblindness and gender are independent characteristics.
    Ha:  Colorblindness and gender aren't related in any way.

d) 

H0:  Colorblindness and gender are independent characteristics.
      Ha:  Colorblindness and gender are related in some way.

Question 4

5 / 5 points

A golfer wished to find a ball that would travel more than 160 yards when hit with his 7-iron with a club speed of 90 miles per hour. He had a golf equipment lab test a low-compression ball by having a robot swing his club 8 times at the required speed. State the null and alternative hypotheses for this test.

Question options:

a) 

H0:  µ = 160; Ha:  µ > 150

b) 

H0:  µ = 150; Ha:  µ > 150

c) 

H0:  µ = 160; Ha:  µ > 160

d) 

H0:  µ = 140; Ha:  µ > 160

Question 5

5 / 5 points

One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
 

 

Colorblind

Not Colorblind

Total

Male

 8

52

 60

Female

 2

38

 40

Total

10

90

100


 
Find the value of the χ2 statistic for the data.

Question options:

a) 

1.463

b) 

1.852

c) 

1.947

d) 

1.949

Question 6

5 / 5 points

One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
 

 

Colorblind

Not Colorblind

Total

Male

7

53

 60

Female

1

39

 40

Total

8

92

100


 
Find the value of the χ2 statistic for the chart data.

Question options:

a) 

1.325

b) 

1.318

c) 

1.286

d) 

1.264

Question 7

5 / 5 points

A 95% confidence interval for the mean of a normal population is found to be 13.2 < µ < 22.4. What is the margin of error?

Question options:

a) 

4.6

b) 

4.4

c) 

4.2

d) 

5.6

Question 8

5 / 5 points

The following data were analyzed using one-way analysis of variance.
 

A

B

C

24

27

19

26

23

31

31

29

27

28

31

22


 
Which one of the following statements is correct?

Question options:

a) 

The purpose of the analysis is to determine whether the groups A, B, and C are independent.

b) 

The purpose of the analysis is to test the hypothesis that the population means of the three groups are equal.

c) 

The purpose of the analysis is to test the hypothesis that the population variances of the three groups are equal.

d) 

The purpose of the analysis is to test the hypothesis that the sample means of the three groups are equal.

Question 9

5 / 5 points

A golfer wished to find a ball that would travel more than 180 yards when hit with his 5-iron with a club speed of 90 miles per hour. He had a golf equipment lab test a low-compression ball by having a robot swing his club 7 times at the required speed. State the null and alternative hypotheses for this test.

Question options:

a) 

H0:  µ = 180; Ha:  µ > 180

b) 

H0:  µ > 180; Ha:  µ > 180

c) 

H0:  µ < 180; Ha:  µ > 180

d) 

H0:  µ = 180; Ha:  µ < 180

Question 10

5 / 5 points

A 95% confidence interval for the mean of a normal population is found to be 17.6 < µ < 23.6. What is the margin of error?

Question options:

a) 

2.0

b) 

2.7

c) 

3.0

d) 

4.0

Question 11

5 / 5 points

Which of the following statements is true?

Question options:

a) 

The p distribution can't be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.

b) 

The t distribution can be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.

c) 

The t distribution can't be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.

d) 

The p distribution can be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.

Question 12

5 / 5 points

One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
 

 

Colorblind

Not Colorblind

Total

Male

 8

52

 60

Female

 2

38

 40

Total

10

90

100


 
If gender and colorblindness are independent, find the expected frequencies of colorblindness and non-colorblindness among 60 males. (Note: To answer this question, it may help to create your own 2 X 2 table of expected frequencies, based on the data for the random sample.)

Question options:

a) 

Male Colorblind 6.0; Male Not Colorblind 54.0

b) 

Male Colorblind 7.0; Male Not Colorblind 53.0

c) 

Male Colorblind 8.0; Male Not Colorblind 52.0

d) 

Male Colorblind 6.0; Male Not Colorblind 53.0

Question 13

5 / 5 points

One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.

 

 

Colorblind

Not Colorblind

Total

Male

7

53

60

Female

1

39

40

Total

8

92

100


 
If gender and colorblindness are independent, find the expected values corresponding to the female combinations of gender and colorblindness.

Question options:

a) 

Colorblind Female 4.8; Not Colorblind Female 55.2

b) 

Colorblind Female 3.2; Not Colorblind Female 36.8

c) 

Colorblind Female 4.8; Not Colorblind Female 35.2

d) 

Colorblind Female 3.8; Not Colorblind Female 36.2

Question 14

5 / 5 points

The critical value of χ2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the χ2 statistic in a test for the dependence of colorblindness on gender had been 4.613, state your conclusion about the relationship between gender and colorblindness.

Question options:

a) 

Reject H0. There's not sufficient evidence to support the claim that gender and colorblindness are related.

b) 

Reject H0. There's sufficient evidence to support the claim that gender and colorblindness are related.

c) 

Don't Reject H0. There's sufficient evidence to support the claim that gender and colorblindness are related.

d) 

Don't Reject H0. There's not sufficient evidence to support the claim that gender and colorblindness are related.

Question 15

5 / 5 points

State the null and alternative hypothesis for the testing whether colorblindness and gender are related.

Question options:

a) 

H0:  Colorblindness and gender are dependent characteristics.
    Ha:  Colorblindness and gender are related in some way.

b) 

H0:  Colorblindness and gender are independent characteristics.
    Ha:  Colorblindness and gender aren't related in any way.

c) 

H0:  Colorblindness and gender are dependent characteristics.
    Ha:  Colorblindness and gender aren't related in any way.

d) 

H0:  Colorblindness and gender are independent characteristics.
      Ha:  Colorblindness and gender are related in some way.

Question 16

5 / 5 points

A large test statistic F tells us that the sample means _______ the data within the individual samples, which would be unlikely if the populations means really were equal (as the null hypothesis claims).

Question options:

a) 

differ more than

b) 

differ less than

c) 

are equal to

d) 

don't vary with

Question 17

5 / 5 points

The margin of error in estimating the population mean of a normal population is E = 9.3 when the sample size is 15. If the sample size had been 18 and the sample standard deviation didn't change, would the margin of error be larger or smaller than 9.3? Explain your answer.

Question options:

a) 

Smaller. E decreases as the square root of the sample size gets larger.

b) 

Smaller. E increases as the square root of the sample size gets larger.

c) 

Larger. E decreases as the square root of the sample size gets larger.

d) 

Larger. E increases as the square root of the sample size gets larger.

Question 18

0 / 5 points

Data from 8 robot swings of a 7-iron at 90 miles per hour resulted in a sample mean of 163.2 yards with a sample standard deviation of 5.8 yards. Assuming normality, carry out a hypothesis test at the 0.05 significance level to determine whether the ball meets the golfer's required average of more than 160 yards per swing.  Use the partial t-table below to solve this problem.
 

 

Area in one tail

 

 

0.025

0.05

 

 

Area in two tails

 

Degrees of Freedom     n - 1

0.05

0.10

     6

2.447

1.943

     7

2.365

1.895

     8

2.306

1.860

     9

2.262

1.833

    10

2.228

1.812

    11

2.201

1.796

    12

2.179

1.782


 

Question options:

a) 

Don't reject the null hypothesis. The data don't provide sufficient evidence that the average distance is greater than 160 yards.

b) 

Reject the null hypothesis. The data does provide sufficient evidence that the average distance is greater than 160 yards.

c) 

t = 1.2334; Critical value = 1.992

d) 

There's insufficient information to answer this question.

Question 19

5 / 5 points

One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
 

 

Colorblind

Not Colorblind

Total

Male

7

53

 60

Female

1

39

 40

Total

8

92

100


 
If gender and colorblindness are independent, find the expected values corresponding to the male combinations of gender and colorblindness.

Question options:

a) 

Colorblind Male 4.8; Not Colorblind Male 55.2

b) 

Colorblind Male 6.8; Not Colorblind Male 53.2

c) 

Colorblind Male 4.8; Not Colorblind Male 55.4

d) 

Colorblind Male 4.8; Not Colorblind Male 56.2

Question 20

5 / 5 points

Which of the following statements is true?

Question options:

a) 

The t distribution can be used when finding a confidence interval for the population mean whenever the sample size is small.

b) 

The p distribution can be used when finding a confidence interval for the population mean whenever the sample size is small.

c) 

The t distribution can't be used when finding a confidence interval for the population mean whenever the sample size is small.

d) 

The p distribution can't be used when finding a confidence interval for the sample mean whenever the sample size is small.


  

 

 

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