Question 6 (this question has three parts (a), (b) & (c))
Covariance matrix
|
A |
B |
C |
|
|
B |
-0.086 |
- |
- |
|
C |
0.056 |
-0.0457 |
- |
|
Market |
0.023 |
-0.0781 |
0.0354 |
Standard deviation table
|
A |
B |
C |
Market |
|
32.25% |
48.25% |
25.24% |
23.25% |
(Marks 1 x 6 = 6)
(Marks 1 x 3 = 3)
(Mark 1)
In: Finance
At an auto parts place, the inspection time for a vehicle is approximately normally distributed with the mean 25 minutes and the standard deviation 3 minutes.
1) What is the probability that a randomly selected car’s inspection time is between 20 and 31 minutes? Round your answer to three decimal places.
2) The owner of this auto parts places will give gift card to customer if his car takes more than the longest 5% of the inspection time. What is the required inspection time to get a gift card? Round your answer to three decimal places.
3) This place also offers free car wash, and the relationship between car’s inspection time and washing time can be written as
inspection time = 1.5 × washing time + 2.5
What are the mean and variance of total {inspection and washing} time.
In: Statistics and Probability
1. The concentration of particles in a suspension is 49 per mL. A 5 mL volume of the suspension is withdrawn.
What is the probability that the number of particles withdrawn will be between 235 and 265?
2. a sample of 100 steel wires the average breaking strength is 46 kN, with a standard deviation of 2 kN.
Find a 95% confidence interval for the mean breaking strength of this type of wire. Round the answers to three decimal places.
The 95% confidence interval is (_,_ ).
Find a 99% confidence interval for the mean breaking strength of this type of wire. Round the answers to three decimal places.
The 99% confidence interval is (_,_ ).
An engineer claims that the mean breaking strength is between 45.7 kN and 46.3 kN. With what level of confidence can this statement be made? Express the answer as a percent and round to two decimal places.
The level of confidence is _%.
In: Statistics and Probability
A new form of cognitive therapy has been developed to treat the symptoms of depression. To determine the effectiveness of the treatment, one group of individuals was exposed to the experimental treatment (Treatment Group) and a second unique group was not exposed to the new treatment (Control Group). The values below represent the Beck Depression Inventory (BDI) scores for the groups. The BDI is a widely used tool for screening depression, and higher scores indicate higher reported levels of depression.
Treatment Group
14 14 14 15 15 17 17 18 18 19
20 20 20 21 22 23 23 23 24 26
26 26 26 27 27 28 28 29 30 30
Control Group
15 15 17 19 19 20 21 22 22 23
24 24 24 24 24 25 25 25 26 26
27 27 27 29 29 29 30 31 31 32
34 34
1. What is the mean BDI score for the treatment group?
2.What is the mean BDI score for the control group?
3.What is the sum of squared deviations for the Treatment Group?
4.What is the sum of squared deviations for the Control Group?
5.Conduct a hypothesis test to determine whether the sample data provide evidence for a difference in the respective populations. Use a two-tailed test and an alpha level of .05. Be sure to include all steps in the hypothesis testing process. Report your findings in the following format:
Step 1
Ho:
Step 2
Identify critical value
Step 3
Report pooled variance
Report error term
Report test statistic (t score)
Step 4
Make a decision
Please show your work step by step so I can understand please and
thank you! I will rate!
A new form of cognitive therapy has been developed to treat the symptoms of depression. To determine the effectiveness of the treatment, one group of individuals was exposed to the experimental treatment (Treatment Group) and a second unique group was not exposed to the new treatment (Control Group). The values below represent the Beck Depression Inventory (BDI) scores for the groups. The BDI is a widely used tool for screening depression, and higher scores indicate higher reported levels of depression.
Treatment Group
14 14 14 15 15 17 17 18 18 19
20 20 20 21 22 23 23 23 24 26
26 26 26 27 27 28 28 29 30 30
Control Group
15 15 17 19 19 20 21 22 22 23
24 24 24 24 24 25 25 25 26 26
27 27 27 29 29 29 30 31 31 32
34 34
1. What is the mean BDI score for the treatment group?
2.What is the mean BDI score for the control group?
3.What is the sum of squared deviations for the Treatment Group?
4.What is the sum of squared deviations for the Control Group?
5.Conduct a hypothesis test to determine whether the sample data provide evidence for a difference in the respective populations. Use a two-tailed test and an alpha level of .05. Be sure to include all steps in the hypothesis testing process. Report your findings in the following format:
Step 1
Ho:
Step 2
Identify critical value
Step 3
Report pooled variance
Report error term
Report test statistic (t score)
Step 4
Make a decision
Please show your work step by step so I can understand please and
thank you! I will rate!
In: Statistics and Probability
A new form of cognitive therapy has been developed to treat the symptoms of depression. To determine the effectiveness of the treatment, one group of individuals was exposed to the experimental treatment (Treatment Group) and a second unique group was not exposed to the new treatment (Control Group). The values below represent the Beck Depression Inventory (BDI) scores for the groups. The BDI is a widely used tool for screening depression, and higher scores indicate higher reported levels of depression.
Treatment Group
14 14 14 15 15 17 17 18 18 19
20 20 20 21 22 23 23 23 24 26
26 26 26 27 27 28 28 29 30 30
Control Group
15 15 17 19 19 20 21 22 22 23
24 24 24 24 24 25 25 25 26 26
27 27 27 29 29 29 30 31 31 32
34 34
1. What is the mean BDI score for the treatment group?
2.What is the mean BDI score for the control group?
3.What is the sum of squared deviations for the Treatment Group?
4.What is the sum of squared deviations for the Control Group?
5.Conduct a hypothesis test to determine whether the sample data provide evidence for a difference in the respective populations. Use a two-tailed test and an alpha level of .05. Be sure to include all steps in the hypothesis testing process. Report your findings in the following format:
Step 1
Ho:
Step 2
Identify critical value
Step 3
Report pooled variance
Report error term
Report test statistic (t score)
Step 4
Make a decision
Please show your work step by step so I can understand please and
thank you! I will rate!
A new form of cognitive therapy has been developed to treat the symptoms of depression. To determine the effectiveness of the treatment, one group of individuals was exposed to the experimental treatment (Treatment Group) and a second unique group was not exposed to the new treatment (Control Group). The values below represent the Beck Depression Inventory (BDI) scores for the groups. The BDI is a widely used tool for screening depression, and higher scores indicate higher reported levels of depression.
Treatment Group
14 14 14 15 15 17 17 18 18 19
20 20 20 21 22 23 23 23 24 26
26 26 26 27 27 28 28 29 30 30
Control Group
15 15 17 19 19 20 21 22 22 23
24 24 24 24 24 25 25 25 26 26
27 27 27 29 29 29 30 31 31 32
34 34
1. What is the mean BDI score for the treatment group?
2.What is the mean BDI score for the control group?
3.What is the sum of squared deviations for the Treatment Group?
4.What is the sum of squared deviations for the Control Group?
5.Conduct a hypothesis test to determine whether the sample data provide evidence for a difference in the respective populations. Use a two-tailed test and an alpha level of .05. Be sure to include all steps in the hypothesis testing process. Report your findings in the following format:
Step 1
Ho:
Step 2
Identify critical value
Step 3
Report pooled variance
Report error term
Report test statistic (t score)
Step 4
Make a decision
Please show your work step by step so I can understand please and
thank you! I will rate!
In: Statistics and Probability
16. Suppose you run a between-subjects experiment in which 11 subjects are randomly selected from the same parent population. 5 subjects are assigned to the control group and 6 subjects are assigned to the experimental group. The subjects in the experimental group are given an experimental drug that is supposed improve their coordination. After giving the experimental group the drug, you measure the coordination of all 11 subjects on a scale for which a higher score means better coordination. The coordination scores for 5 subjects in the control group are 49, 53, 67, 81, 43. The coordination scores for the 6 subjects in the experimental group are 58, 63, 92, 80, 67, 74. What are the degrees of freedom for the control group, and the experimental group, as well as the total degrees of freedom for this analysis.
17. What is the value of the pooled variance for the problem described in Question 16?
18. What is the value of sdifferrence for the data in Question 16?
19. Calculate the t statistic for the data in Question 16.
20. Does your t statistic allow you to reject that the null hypothesis that the drug had no effect in favor of your experimental hypothesis that the drug improves coordination at an alpha level of 0.05? What about at an alpha level of 0.01?
In: Statistics and Probability
The manufacturer of hardness testing equipment uses steel-ball indenters to penetrate metal that is being tested. However, the manufacturer thinks it would be better to use a diamond indenter so that all types of metal can be tested. Because of differences between the two types of indenters, it is suspected that the two methods will produce different hardness readings. The metal specimens to be tested are large enough so that two indentions can be made. Therefore, the manufacturer uses both indenters on each specimen and compares the hardness readings. Construct a 95% confidence interval to judge whether the two indenters result in different measurements.
Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.
Specimen 1 2 3 4 5 6 7 8 9
Steel Ball 51 57 61 70 68 54 65 51 53
Diamond 53 56 61 74 69 55 68 51 56
Construct a 95% confidence interval to judge whether the two indenters result in different measurements, where the differences are computed as 'diamond minus steel ball'.
The uppper bound is _______?
The lower bound is _________?
The test statistic is __________?
In: Statistics and Probability
The manufacturer of hardness testing equipment uses steel-ball indenters to penetrate metal that is being tested. However, the manufacturer thinks it would be better to use a diamond indenter so that all types of metal can be tested. Because of differences between the two types of indenters, it is suspected that the two methods will produce different hardness readings. The metal specimens to be tested are large enough so that two indentions can be made. Therefore, the manufacturer uses both indenters on each specimen and compares the hardness readings. Construct a 95% confidence interval to judge whether the two indenters result in different measurements.
Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.
Specimen Steel ball Diamond
1 50 52
2 57 55
3 61 63
4 70 74
5 68 69
6 54 55
7 65 68
8 51 51
9 53 56
Construct a 95% confidence interval to judge whether the two indenters result in different measurements, where the differences are computed as 'diamond minus steel ball'.
The lower bound is
The upper bound is
(Round to the nearest tenth as needed.)
In: Statistics and Probability
The manufacturer of hardness testing equipment uses steel-ball indenters to penetrate metal that is being tested. However, the manufacturer thinks it would be better to use a diamond indenter so that all types of metal can be tested. Because of differences between the two types of indenters, it is suspected that the two methods will produce different hardness readings. The metal specimens to be tested are large enough so that two indentions can be made. Therefore, the manufacturer uses both indenters on each specimen and compares the hardness readings. Construct a 95% confidence interval to judge whether the two indenters result in different measurements.
Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.
Specimen Steel ball Diamond
1 51 53
2 57 55
3 61 63
4 71 74
5 68 69
6 54 55
7 65 68
8 51 51
9 53 56
Construct a 95% confidence interval to judge whether the two indenters result in different measurements, where the differences are computed as 'diamond minus steel ball'.
The lower bound is __?__ .
The upper bound is __?__.
(Round to the nearest tenth as needed.)
In: Statistics and Probability
I would like to know if the sex of a math student is a statistically significant factor in predicting average math exam scores. The following lists are exam scores for a math exam, separated by sex.
male 89 33 104 48 90 80 98 32 98 55 75 74 73 90 105 47 48 67 99 103 63
female 99 80 81 88 94 83 70 42 78 75
Perform a hypothesis test to determine whether the sex of a math student is statistically significant for performance on math tests. In other words, is there a statistically significant difference between the scores of these two groups of students?
(a) State the null and alternative hypotheses. Also, state the meaning of your parameters.
(b) Perform the test. Use α = .05. Show your work. Clearly indicate the value of the test statistic. Be sure to mention the value of df if it is relevant. Also, make sure you clearly state your final answer to the question above.
(c) Compute an appropriate 95% confidence interval that would confirm your final answer from part (b). Explain why it confirms that answer.
In: Math