automobile manufacturer claims that they're paying his debt 36.7 miles per gallon rating Independent Taxi firm has been contracted to MP3 to stand texting Chrome and family leave MCG of 36.3 with a standard deviation of 2.1 is there sufficient evidence such a 0.025 level of Ativan underperform the manufacturers in PG rating

1. What is the difference between a corporate strategy and a business strategy?

2.How are the business strategy typologies by Porter and Miles & Snow similar? How are they different?

3.Why might one expect the performance level of midsize business units to be lower than the performance level of either small or large business units?

Automobile insurance companies take many factors into consideration when setting rates. These factors include age, marital status and miles driven per year. To determine the effect of gender, a random sample of young (under 25, with at least 2 years of driving experience) male and female drivers was surveyed. Each was asked how many miles he or she had driven in the past year. The distances (in thousands of miles) are stored in stacked format (column 1= driving distances and column 2 identifies gender where 1=male and 2=female). (Assume equal variances.) (a) Can we conclude that male & female drivers differ in the numbers of miles driven per year? (you need to compute the sample means and sample standard deviations for each gender in the Excel Workbook that comes with this exercise. Use ”=AVERAGE()” and ”=STDEV()” formulas. This also applies to exercises further below.) (b) Estimate with 95% confidence the difference in mean distance driven by male and female drivers.

Decision

You are considering the purchase of a new vehicle. There are two options for the auto acquisition: a traditional gas-powered auto or a hybrid auto. Based on the information provided below and using net present value (NPV), you will be evaluating the two options and making a recommendation. Note: this scenario is a least cost decision. Since the decision to buy a car will only involve costs, you will be choosing the option with the highest NPV (which in this case, will be the project with the LEAST negative NPV). The assumed WACC is 10%.

Traditional Gas-Powered Auto:

                        Project Life: The autos are going to be kept for 7 years before being sold.

Cost of Auto:   $18,000

Annual Maintenance Cost: Each year, maintenance costs will be a fixed $300.

Gas Cost: The cost of gas is estimated to be an average of $3.30 per gallon over the next 7 years. The auto gets an average of 30 miles to the gallon. The auto is to be driven 16,000 miles per year.

Salvage Value: The car has an estimated salvage value of $4,000 at the end of 7 years.

Hybrid Auto:

                        Project Life: The autos are going to be kept for 7 years before being sold.

Cost of Auto:   $24,000

Annual Maintenance Cost: Each year, maintenance costs will be a fixed $450 (hybrid maintenance costs are higher due to more complex technology).

Gas Cost: The cost of gas is estimated to be an average of $3.30 per gallon over the next 7 years. The auto gets an average of 55 miles to the gallon. The auto is to be driven 16,000 miles per year.

Salvage Value: The car has an estimated salvage value of $7,000 at the end of 7 years.

Tax Credit: The US government encourages the purchase of more fuel-efficient autos, and has offered a $1,000 tax credit in the year of purchase of a qualifying vehicle. Note: The tax credit represents a cash inflow, as it represents cash saved on taxes. Assume the tax credit is taken at the END of the first year of ownership.

Required:

1. Calculate the NPV for both auto purchases.
2. Make a recommendation for which car you would purchase.
3. Assume gas prices rise to an average of $4.50 per gallon. Recalculate the NPVs and make a recommendation.

Cognitive-based therapy (CBT) and family-based therapy (FBT) are two different treatments for anorexia. In an experimental study, forty-six anorexic teenage girls were randomly assigned to two groups. One group, consisting of n1 = 29 individuals, received CBT, and the other group, consisting of n2 = 17 individuals, received FBT. Weight of each individual is measured twice, once at the beginning and once at the end of the study period. The variable of interest is the weight change, i.e. weight after therapy minus weight before therapy. The data collected from the two samples are given below.

cognitive = c(1.7, 0.7, -0.1, -0.7, -3.5, 14.9, 3.5, 17.1,  -7.6, 1.6, 11.7, 6.1,

    1.1, -4.0, 20.9, -9.1, 2.1, -1.4, 1.4, -0.3, -3.7, -0.8, 2.4, 12.6, 1.9, 3.9,

    0.1, 15.4, -0.7)

family = c(11.4, 11.0,  5.5,  9.4, 13.6, -2.9, -0.1,  7.4,  21.5, -5.3, -3.8, 13.4,

    13.1,  9.0,  3.9,  5.7, 10.7)

Note that a positive weight change (weight gain) is generally good for anorexia patients. Let μ1 be the population mean weight change in the CBT group, and μ2 the population mean weight change in the FBT group. The goal is to conduct statistical inference on the difference μ1 − μ2

-

4. Two-sample t-test relies on the assumption that the two samples are either large enough (n1 ≥ 30 and n2 ≥ 30) or coming from normal distributions. In the context of this problem, neither of the two samples is large enough.

(a) Check the normality assumption for both samples using the normal quantile-quantile plot. Re- member that you can do this in R using the qqnorm command.

(b) Suppose one thinks that the normality assumption does not hold for this data set, hence does not trust the results provided in the two-sample t-test. Suggest a different hypothesis testing procedure that does not rely on the normality assumption. (Note: You don’t have to carry out the test.

1. On the basis of a physical examination, a doctor determines the probability of no tumour   (event labelled C for ‘clear’), a benign tumour (B) or a malignant tumour (M) as 0.7, 0.2 and 0.1 respectively.

A further, in depth, test is conducted on the patient which can yield either a negative (N) result or positive (P). The test gives a negative result with probability 0.9 if no tumour is present (i.e. P(N|C) = 0.9). The test gives a negative result with probability 0.8 if there is a benign tumour and 0.2 if there is a malignant tumour.

(i) Given this information calculate the joint and marginal probabilities and display in the table below.

2. What is the marginal probability the test result will be negative?
3. Obtain the posterior probability distribution for the patient when the test result is

            a) positive,   b) negative

4. Comment on how the test results change the doctor’s view of the presence of a tumour.

2. (i) A continuous variable X defined on the interval (1, ∞) has p.d.f given by f(x) = 1/x²

Derive the corresponding cumulative density function and graph it

(ii) Can the function f(x) = 1/x² define a p.d.f over the interval (2, ∞)? Explain your answer.

3. In the context of a discrete variable, X, show that the formula for variance of the variable can be written as Var(X) = E(X²) – [E(X)]²

4. Suppose that f(x) = 1/5 , x = 1, 2, 3, 4, 5 and zero elsewhere is the p.d.f. of the discrete random variable X. Compute E(X) and E(X²).

Use these results to find E[(X+2)²]

5. In question 4, calculate Var(X).

Question 1 A contractor is interested in the total cost of a project for which he intends to bid. He estimates that materials will cost P25000 and that his labour will cost P900 per day. The contractor then formulates the probability distribution for completion time (X), in days, as given in the following table. Completion time in days (X) 10 11 12 13 14 P(X=x) 0.1 0.3 0.3 0.2 0.1 a) Determine the total cost function C for the project. b) Find the mean and variance for completion time X. c) Find the mean, variance and standard deviation for the total cost C.

For Part 2 of this assignment, you will use the “Assignment 1 – Linear Kinematics Data” excel file. In the data set you are provided with vertical position and time data for a person’s vertical center of mass motion for an unspecified movement task.

You will utilize excel in all (well, some…) of its glory to calculate the vertical velocity and vertical acceleration data from the position and time data provided in the excel file. Again you will use the First Central Difference Method to calculate velocity and acceleration at each frame. Once the velocity and acceleration data have been calculated, plot the position, velocity, and acceleration data against time, either as one graph per variable or all three variables on one graph (using primary and secondary axes). Be sure to label the graphs neatly and appropriately such that you would be confident including them in a formal presentation based on the instructions provided in the tutorials.

1. Between 1 and 1.5 seconds, what direction is the person moving? Are they speeding up, slowing down, or both during this time period?
2. Between 1.75 and 2 seconds, was the acceleration positive, negative, or both? In addition, was the person moving upward, downward, or both during this time period?
3. At approximately what time is the person moving at the fastest velocity and in what direction are they moving at this time?
4. Based on your understanding of the position-velocity-acceleration relationship, what human movement does this data represent assuming the data represent the entire movement task from start to finish?