A legal researcher wanted to measure the effect of the length of a criminal trial on the length of jury deliberation. He observed in a sample of 10 randomly selected courtroom trials the following data on length of trial (in days) and length of jury deliberation (in hours). Using the table below, complete the followiwng steps:

Step 1: Calculate the regression and Y-intercept by calculating N, the sum of X, the sum of Y, the sum of X-squared, the sum of Y-squared, and the sum of XY.

Step 2: Calculate the mean of X and the mean of Y.

Step 3: Calculate SSx, SSy, and SP

Step 4: Determine the regression line

Step 5: Predict the length of jury deliberation for a recently completed trial that lasts six days.

Step 6: Find the coefficient of determination and nondetermination. What do they mean?

Step 7: Construct and analysis of variance table.

Please no minitab answers. I would prefer the formulas written out step by step for each number so I can understand how to get to the answer.

Find the inverse Laplace transform for

1 / ((s^2+1)(s+1))

1. conic memory is a type of memory that holds visual information for about half a second (0.5 seconds). To demonstrate this type of memory, participants were shown three rows of four letters for 50 milliseconds. They were then asked to recall as many letters as possible, with a 0-, 0.5-, or 1.0-second delay before responding. Researchers hypothesized that longer delays would result in poorer recall. The number of letters correctly recalled is given in the table.

(a) Complete the F-table. (Round your values for MS and F to two decimal places.)

(b) Compute Tukey's HSD post hoc test and interpret the results. (Assume alpha equal to 0.05. Round your answer to two decimal places.)

The critical value is    for each pairwise comparison.

c) Which of the comparisons had significant differences? (Select all that apply.)

a. Recall following no delay was significantly different from recall following a one second delay.

b. Recall following a half second delay was significantly different from recall following a one second delay.

c. The null hypothesis of no difference should be retained because none of the pairwise comparisons demonstrate a significant difference.

d. Recall following no delay was significantly different from recall following a half second delay.

2. An educator wants to evaluate four different methods aimed at reducing the time children spend "off task" in the classroom. To test these methods, she implements one method in each of four similar classrooms and records the time spent off task (in minutes) in each classroom. The results are given in the table.

(a) Complete the F-table. (Round your answers to two decimal places.)

3. After computing a one-way within-subjects analysis of variance at a 0.1 level of significance, a psychologist begins to calculate a Bonferroni procedure. If she will make a 5 pairwise comparisons, what will be the testwise alpha?

The newest invention is a three-sided die. On any roll of this die, the result is 1 with probability 1/2, 2 with probability 1/4, and 3 with probability 1/4.

Consider a sequence of six independent rolls of this die.

A. Find the probability that exactly two of the rolls result in a 3.

B. Given that exactly two of the six rolls resulted in a 1, find the probability that the first roll resulted in a 1.

C. We are told that exactly three of the rolls resulted in a 1 and exactly three rolls resulted in a 2. Given this information, find the probability that the six rolls resulted in the sequence (1,2,1,2,1,2).

Q.1 Marks 2 (CLO 3)

From the following data, you are required to: -

(a) Fit the regression line Y on X and predict Y if x = 20

(b) Fit the regression line X on Y and predict X if y = 10

Note : Answers should be in Word or Excel Format

A clinical trial is run to compare weight loss programs and participants are randomly assigned to one of the four comparison programs and are counseled on the details of the assigned program. Three popular weight loss programs were considered: the low calorie diet, the low fat diet, and the low carbohydrate diet . For comparison purposes, a fourth group is considered as a control group. Participants in the fourth group are told that they are participating in a study of healthy behaviors. After 8 weeks, each patient's weight is again measured and the difference in weights is computed by subtracting the 8-week weight from the baseline weight. Positive differences indicate weight losses and negative differences indicate weight gains. Observed weight losses are shown below.

1. Using ANOVA determine if there are differences in weight loss among four groups:

• Set up null and alternative hypothesis
• Calculate the appropriate test statistic (Use ANOVA in excel)
• Provide interpretation of your results

2. Using ANOVA determine if there are differences in weight loss among ‘dieting’ groups (basically exclude the control group from the hypothesis testing)

• Set up null and alternative hypothesis
• Calculate the appropriate test statistic (Use ANOVA in excel)
• Provide interpretation of your results

3. What overall conclusions researchers can make based on the testing results from parts a and b?

A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $1,000s). He collects data on 20 individuals. A portion of the data is as follows:

Salary   Education
40   4
73   1
99   7
57   1
83   8
76   4
109   6
49   0
31   4
32   4
91   2
40   4
65   6
71   2
166   5
61   0
88   1
59   4
132   9
25   0

a. Find the sample regression equation for the model: Salary = β₀ + β₁Education + ε. (Round answers to 2 decimal places.)

Salaryˆ=

+ Education

b. Interpret the coefficient for Education.

• As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $8,590.

• As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $8,590.

• As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $6,220.

• As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $6,220.

c. What is the predicted salary for an individual who completed 5 years of higher education? (Round coefficient estimates to at least 4 decimal places and final answer to the nearest whole number.)

Salaryˆ               $

(c) Compute the sample correlation coefficient r for each of the following data sets and show that r is the same for both. (Use 3 decimal places.) (i) x 6 1 9 y 4 2 5

(ii)x 4 2 5 y6 1 9

What is the standard form of the equation of the parabola with the focus (−1,3) and the directrix x=9?

Select the correct answer below:

a) (x+1)2=−12(y−6)

b) (y−3)2=−20(x−4)

c) (x−9)2=8(y−1)

d)(y−3)2=20(x−4)

please show work and what is the correct answer? thanks

Consider the following project’s after-tax cash flow and the expected annual inflation rates during the project period.

1. Convert the cash flows in actual dollars into equivalent constant dollars with the base year 0. (complete the table for constant dollars cash flow)
2. If the annual real interest rate is 15%, what is the present worth of the cash flow? Is this project acceptable?