A lumber company has just taken delivery on a shipment of 10,000 2 ✕ 4 boards. Suppose that 10% of these boards (1000) are actually too green to be used in first-quality construction. Two boards are selected at random, one after the other. Let A = {the first board is green} and B = {the second board is green}.
(a) Compute P(A), P(B), and P(A ∩ B) (a tree diagram might help). (Round your answer for P(A ∩ B) to five decimal places.)

P(A) =
P(B) =
P(A ∩ B) =

Are A and B independent?
Yes, the two events are independent.No, the two events are not independent.    
(b) With A and B independent and P(A) = P(B) = 0.1, what is P(A ∩ B)?


How much difference is there between this answer and P(A ∩ B) in part (a)?
There is no difference.There is very little difference.    There is a very large difference.
For purposes of calculating P(A ∩ B), can we assume that A and B of part (a) are independent to obtain essentially the correct probability?
YesNo    
(c) Suppose the lot consists of ten boards, of which one are green. Does the assumption of independence now yield approximately the correct answer for P(A ∩ B)?
YesNo    
What is the critical difference between the situation here and that of part (a)?
The critical difference is that the population size in part (a) is small compared to the random sample of two boards.The critical difference is that the percentage of green boards is smaller in part (a).    The critical difference is that the percentage of green boards is larger in part (a).The critical difference is that the population size in part (a) is huge compared to the random sample of two boards.
When do you think that an independence assumption would be valid in obtaining an approximately correct answer to P(A ∩ B)?
This assumption would be valid when the population is much larger than the sample size.This assumption would be valid when the sample size is very large.    This assumption would be valid when there are fewer green boards in the sample.This assumption would be valid when there are more green boards in the sample.

The following data are the monthly salaries y and the grade point averages x for students who obtained a bachelor's degree in business administration.

The estimated regression equation for these data is y=-674.3+1,351.4x and MSE=395,912.

Use Table 1 of Appendix B.

a. Develop a point estimate of the starting salary for a student with a GPA of 3.0 (to 1 decimal).

b. Develop a 95% confidence interval for the mean starting salary for all students with a 3.0 GPA (to 2 decimals).

(  ,  )

c. Develop a  prediction interval for Ryan Dailey, a student with a GPA of 3.0 (to 2 decimals).

(  ,  )

d. Discuss the differences in your answers to parts (b) and (c).

An experiment has been conducted for four treatments with eight blocks. Complete the following analysis of variance table (to 2 decimals, if necessary and p-value to 4 decimals). If your answer is zero enter "0".

Use  = .05 to test for any significant differences.

Consider the following data for two variables, x and y.

(a) Develop an estimated regression equation for the data of the form  ŷ = b₀ + b₁x.  (Round b₀ to one decimal place and b₁ to three decimal places.)

ŷ =

(b) Use the results from part (a) to test for a significant relationship between x and y. Use α = 0.05. Find the value of the test statistic. (Round your answer to two decimal places.)

F =

Find the p-value. (Round your answer to three decimal places.)

p-value =

(C) Develop an estimated regression equation for the data of the form ŷ = b₀ + b₁x + b₂x².  (Round b₀ to one decimal place and b₁ to two decimal places and b₂ to four decimal places.)

ŷ =

(D) Use the results from part (C) to test for a significant relationship between x, x²,  and y. Use α = 0.05. Is the relationship between x, x²,  and y significant?

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

Use the model from part (c) to predict the value of y when x = 25. (Round your answer to three decimal places.)

Consider the following data for two variables, x and y.

(a) Develop an estimated regression equation for the data of the form

ŷ = b₀ + b₁x. (Round b₀ to two decimal places and b₁ to three decimal places.)

ŷ =

(b) Develop an estimated regression equation for the data of the form

ŷ = b₀ + b₁x + b₂x².  (Round b₀ to two decimal places and b₁ to three decimal places and b₂ to four decimal places.)

ŷ =

(c) Use the model from part (b) to predict the value of y when x = 20.  (Round your answer to two decimal places.)

Please read these instructions and answer the questions below.  

Assume that you are a social work practitioner at an agency that provides mental health support services to military veterans. The agency currently serves 396 veterans. Your supervisor asks you to develop a questionnaire and administer a survey to these clients to determine their satisfaction with services and how the agency might improve services. There is a particular concern related to complaints about services to transgender and women clients.  

Your supervisor said:  

“Be sure to include a good representation of our clients by gender! Don’t worry about combat experiences! And we have enough money for participation gift cards for up to 100 clients”.  

Table showing the numbers of clients served by gender and history of combat experiences.

1. Describe how you could go about drawing a convenience sample of veterans/clients to survey.  

2. Describe how you could draw a systematic random sample of these veterans to survey?  

3. Describe how you would draw a disproportional stratified random sample (representing gender) of the veterans to survey? Assuming you have the capacity for 100 participants or so, what would you do?  

4. Explain the motivation for drawing a disproportional stratified random sample—why might you want to do it?  

a die is tested for fairness using Ha : p does not equal 1/6 where p is the proportions of the sixes that occur . Would ubserving 12 sixes in 114 rolls of the die be statistically significant evidence that the true probability of a six is different from 1/6? use 10% significance level.

Answer the following questions based on the information provided below:

You are conducting a study to determine the impact of a new reading intervention on students test scores. You randomly assign 40 students to either the intervention group or the control group (those not participating in the intervention). You also break the students into morning and afternoon classes to determine which is the best time of day to conduct the intervention.

1. What is the dependant variable?

2. What is/are the independent variable(s)?

3. How many cells will there be?

4. If we divide the groups evenly how many students will appear in each cell?

5. What type of design is this? (Again, Be Specific!)

6. Assume that you conduct an ANOVA with 3 groups and 60 subjects (evenly divided between the 3 groups) and receive an F-value of 3.30. How would you write this result in a study? (Be sure to include whether or not it is a significant result)

Inference for one mean

Karen wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 43 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 15.2 and a standard deviation of 1.3. What is the 95% confidence interval for the number of chocolate chips per cookie for Big Chip cookies?

Enter your answers accurate to one decimal place:

_< μ < _

A survey of MBA graduates of a business school obtained data on the first-year salary after graduation and years of work experience prior to obtaining their MBA. The data are given in excel.

1. Run the regression analysis (Include all options). Report the least squares regression line. Give the 95% confidence interval for the least squares estimate of the slope. Report the correlation coefficient. Interpret.  Report the coefficient of determination. Interpret. and  Use the ANOVA output and write out the hypothesis being tested, the test statistic, the critical value, p-value, and fully write out the conclusion.

An article suggests that substrate concentration (mg/cm3) of influent to a reactor is normally distributed with μ = 0.40 and σ = 0.06. (Round your answers to four decimal places.)

a. What is the probability that the concentration exceeds 0.60?

b. What is the probability that the concentration is at most 0.30?

c. How would you characterize the largest 5% of all concentration values?

d. The largest 5% of all concentration values are above = mg/cm³.

An English professor assigns letter grades on a test according to the following scheme.

A: Top 14%14% of scores

B: Scores below the top 14%14% and above the bottom 57%57%

C: Scores below the top 43%43% and above the bottom 24%24%

D: Scores below the top 76%76% and above the bottom 8%8%

F: Bottom 8%8% of scores

Scores on the test are normally distributed with a mean of 69.669.6 and a standard deviation of 99. Find the numerical limits for a D grade.

HOW DO I SOLVE IT ON TI-84PLUS

What is Normal? Give some examples of variables that would have an approximately normal distribution?

1. Suppose the following indexed scores represent performance on a new survey meant to understand an individual’s level of depression. Suppose a score of above 20 represents a depressed individual based on the survey design.  

1. What is the relative frequency of those individuals that represent depressed individuals?
2. What is the median score for the depression scale in this group of individuals?

You are maintaining a collection for fwooper , and are trying to adjust their diet to keep them from gaining or losing too much weight. You know that fwoopers in the wild have a mean mass of 125 grams but other than that you don’t know much else.

The data you collect initially about the fwooper mass is in the excel data table.

fwooper mass (g)

1 143.9

2 141.9

3 122.9

4 106.8

5 120.3

6 163.3

7 126

8 111.7

9 111.1

10 111.8

11 131.5

12 122.2

13 99.1

14 127.4

15 116.4

16 113.6

17 144

18 111.8

19 117.1

20 108.1

21 149.9

22 108.8

23 156.9

24 103.4

1. Are you comparing two sets, one set of data to a known value?

2. If you are comparing one set of data to a known value, do you know the population variance?

3. If you are comparing two sets of data, are they INDEPENDENT or PAIRED?

4. IF the data are independent do you need to do an F-Test?

5. IF you need to do an F-test, record the results here:( if not put N/A and delete)

• F-test Null Hypothesis: -F-test Alternative Hypothesis:

• F-test ratio(calc): - F-test Critical Value:

6. Which type of hypothesis test are you going to do?

One sample Z test one sample t-test homoscedastic t-test

Heteroscededatic t-test paired t-test

7. For your hypothesis test, record the following:

           Null hypothesis: Alternative Hypothesis: test statistic:

           P-value: df= critical value:      

8. Statistical conclusion: Reject null hypothesis or Fail to reject Null hypothesis

9. Biological Conclusion: