We want to compare the mean of the hospital stay by sex at this particular Pennsylvania hospital. Let’s assume that the data are normally distributed and we are assuming that the SD for sexes are equal.    So, is there a difference in the mean hospital stay in Pennsylvania hospital by gender?    (Please include SPSS output here)

State the null and alternative hypotheses.   

What is your test statistics and why?  (no calculation needed)

What were your test statistics results? What is your conclusion?

Please note: the table below might not be needed; however, these are my calculations for Mean and SD for sexes.

1) 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 =  

2)

A statistical program is recommended.

A study investigated the relationship between audit delay (Delay), the length of time from a company's fiscal year-end to the date of the auditor's report, and variables that describe the client and the auditor. Some of the independent variables that were included in this study follow.

A sample of 40 companies provided the following data.

(a)

Develop the estimated regression equation using all of the independent variables. Use x₁ for Industry, x₂ for Public, x₃ for Quality, and x₄ for Finished. (Round your numerical values to two decimal places.)

ŷ =

−5.21x4​−1.80x3​+1.65x2​+12.11x1​+78.83

(b)

Did the estimated regression equation developed in part (a) provide a good fit? Explain. (Use α = 0.05. For purposes of this exercise, consider an adjusted coefficient of determination value high if it is at least 50%.)

Yes, testing for significance shows that the overall model is significant and all the individual independent variables are significant.No, the low value of the adjusted coefficient of determination does not indicate a good fit.    Yes, the low p-value and high value of the adjusted coefficient of determination indicate a good fit.No, testing for significance shows that all independent variables except Public are not significant.

What does this scatter diagram indicate about the relationship between Delay and Finished?

The scatter diagram suggests no relationship between these two variables.The scatter diagram suggests a linear relationship between these two variables.     The scatter diagram suggests a curvilinear relationship between these two variables.

(d)

On the basis of your observations about the relationship between Delay and Finished, use best-subsets regression to develop an alternative estimated regression equation to the one developed in (a) to explain as much of the variability in Delay as possible. Use x₁ for Industry, x₂ for Public, x₃ for Quality, and x₄ for Finished. (Round your numerical values to two decimal places.)

ŷ =

−38.56x4​−2.28x3​+7.45x2​+14.27x1​+113.01

Choose one of the attached data sets and analyze using the techniques discussed in class up to this point. This includes the following: Find the appropriate measure of center. Discuss why the chosen measure is most appropriate. Why did you decide against other possible measures of center? Find the appropriate measure of variation. The measure of variation chosen here should match the measure of center chosen in Part 1. Find the graph(s) needed to appropriately describe the data. These may be done by hand and inserted into the Word document. Define a random variable (X) so that your chosen data set represents values of X. Is your chosen random variable discrete or continuous? Explain how you know. Would the Normal or Binomial distribution be a good fit for the underlying sample distribution of X? If one of them is a good fit, state how you would approximate the distribution parameters. Calculate the probability that a flight will depart early or on-time. Calculate the probability that a flight will arrive late. Calculate the probability that a flight departs late or arrives early. Assume now that the random variable X=Arrival Time is exactly normally distributed with mean m= -2.5 and standard deviation s= 23. Compute the probability of a flight arriving late based on this new information. Does this contradict your answer from Part 8? Write a brief description (250–500 words) of the data set including the discussion required in the points above. Year DAY_OF_MONTH DAY_OF_WEEK DEP_Delay ARR_Delay 2015 13 2 -4 0 2015 13 2 -3 -3 2015 13 2 0 -5 2015 13 2 -7 -1 2015 13 2 8 3 2015 13 2 -1 -5 2015 13 2 3 8 2015 13 2 11 6 2015 13 2 -6 0 2015 13 2 -5 -12 2015 13 2 -8 0 2015 13 2 -4 -2 2015 13 2 -13 -10 2015 13 2 -13 12 2015 13 2 -11 -13 2015 13 2 -14 4 2015 13 2 -16 -1 2015 13 2 -14 2 2015 13 2 -18 -14 2015 13 2 -18 0 2015 13 2 -23 -23 2015 13 2 -23 10 2015 13 2 2 -20 2015 13 2 1 26 2015 13 2 -4 -25 2015 13 2 -6 7 2015 13 2 7 -3 2015 13 2 -8 0 2015 13 2 -8 0 2015 13 2 -4 -2 2015 13 2 -4 -3 2015 13 2 -5 -6 2015 13 2 -13 -9 2015 13 2 -9 6 2015 13 2 -12 -7 2015 13 2 -7 -4 2015 13 2 -12 -9 2015 13 2 1 4 2015 13 2 4 12 2015 13 2 -19 0 2015 13 2 -13 -4 2015 13 2 -19 -17 2015 13 2 3 -18 2015 13 2 12 15 2015 13 2 13 20 2015 13 2 2 12 2015 13 2 0 0 2015 13 2 0 -14 2015 13 2 4 5 2015 13 2 -7 7 2015 13 2 8 8 2015 13 2 9 22 2015 13 2 -1 -5 2015 13 2 -10 1 2015 13 2 -6 0 2015 13 2 -12 2 2015 13 2 -14 -3 2015 13 2 -13 7 2015 13 2 9 1 2015 13 2 -15 -2 2015 13 2 -13 1 2015 13 2 -14 -1 2015 13 2 20 6 2015 13 2 -16 -7 2015 13 2 11 0 2015 13 2 -14 6 2015 13 2 18 1 2015 13 2 -19 -17 2015 13 2 -3 -16 2015 13 2 -4 -2 2015 13 2 0 -1 2015 13 2 -3 -6 2015 13 2 2 -17 2015 13 2 6 7 2015 13 2 6 14 2015 13 2 -6 -13 2015 13 2 1 11 2015 13 2 11 12 2015 13 2 -7 -2 2015 13 2 -10 -4 2015 13 2 -13 0 2015 13 2 9 3 2015 13 2 -13 -4 2015 13 2 -18 3 2015 13 2 -17 0 2015 13 2 -11 0 2015 13 2 -20 -6 2015 13 2 -18 -8 2015 13 2 8 -8 2015 13 2 0 -12 2015 13 2 -20 -10 2015 13 2 -3 -9 2015 13 2 1 6 2015 13 2 -1 -13 2015 13 2 -4 3 2015 13 2 -6 0 2015 13 2 -5 -13 2015 13 2 -8 6 2015 13 2 -10 -17 2015 13 2 -9 9 2015 13 2 -6 -19 2015 13 2 8 13 2015 13 2 -9 -2 2015 13 2 -12 -21 2015 13 2 -15 -16 2015 13 2 -14 -28 2015 13 2 -9 -14 2015 13 2 -17 -2 2015 13 2 -13 4 2015 13 2 -17 -2 2015 13 2 2 6 2015 13 2 -18 -6 2015 13 2 -18 -1 2015 13 2 -16 0 2015 13 2 1 -8 2015 13 2 -4 0 2015 13 2 0 2 2015 13 2 -5 -13 2015 13 2 7 2 2015 13 2 -7 -11 2015 13 2 -7 -7 2015 13 2 -5 -1 2015 13 2 0 -7 2015 13 2 5 7 2015 13 2 -6 -1 2015 13 2 -12 -21 2015 13 2 1 19 2015 13 2 6 2 2015 13 2 -10 -12 2015 13 2 -15 5 2015 13 2 -18 -22 2015 13 2 -16 -24 2015 13 2 -17 -20 2015 13 2 0 -20 2015 13 2 -21 -1 2015 13 2 -18 -1 2015 13 2 5 -4 2015 13 2 1 3 2015 13 2 3 5 2015 13 2 -2 -6 2015 13 2 -1 5 2015 13 2 -2 -6 2015 13 2 -3 -9 2015 13 2 4 10 2015 13 2 3 13 2015 13 2 -11 -12 2015 13 2 9 -9 2015 13 2 -11 1 2015 13 2 -11 -14 2015 13 2 0 -12 2015 13 2 -11 -16 2015 13 2 17 8 2015 13 2 -10 -14 2015 13 2 -11 -4 2015 13 2 0 -18 2015 13 2 -19 -16 2015 13 2 -18 -20 2015 13 2 0 7 2015 13 2 8 11 2015 13 2 -23 -8 2015 13 2 3 -24 2015 13 2 -3 0 2015 13 2 -4 -2 2015 13 2 -6 0 2015 13 2 0 -1 2015 13 2 2 1 2015 13 2 -1 4 2015 13 2 -9 -5 2015 13 2 -9 1 2015 13 2 4 -9 2015 13 2 1 3 2015 13 2 -9 6 2015 13 2 -12 8 2015 13 2 0 -9 2015 13 2 0 -15 2015 13 2 -11 -14 2015 13 2 -14 -4 2015 13 2 -19 -13 2015 13 2 -17 2 2015 13 2 -13 9 2015 13 2 23 4 2015 13 2 8 11 2015 13 2 21 17 2015 13 2 3 1 2015 13 2 4 22 2015 13 2 -2 6 2015 13 2 1 0 2015 13 2 6 24 2015 13 2 7 1 2015 13 2 -9 -2 2015 13 2 -3 -1 2015 13 2 1 0 2015 13 2 -9 -7 2015 13 2 -5 -2 2015 13 2 -11 -9 2015 13 2 -6 8 2015 13 2 -6 -10 2015 13 2 -10 -4 2015 13 2 -13 -1 2015 13 2 -9 -10 2015 13 2 -17 -4 2015 13 2 -6 -11 2015 13 2 -20 -12 2015 13 2 1 6 2015 13 2 -21 -2 2015 13 2 -22 -7 2015 13 2 -2 -7 2015 13 2 0 2 2015 13 2 -4 -20 2015 13 2 -3 -12 2015 13 2 3 4 2015 13 2 -5 -8 2015 13 2 -6 -4 2015 13 2 -3 -7 2015 13 2 -5 -14 2015 13 2 -8 -3 2015 13 2 -12 -4 2015 13 2 -10 -2 2015 13 2 -7 -2 2015 13 2 -16 -4 2015 13 2 1 1 2015 13 2 -14 -7 2015 13 2 -14 1 2015 13 2 -16 -11 2015 13 2 -7 -3 2015 13 2 13 -12 2015 13 2 -17 -14 2015 13 2 -16 -13 2015 13 2 7 5 2015 13 2 0 12 2015 13 2 1 14 2015 13 2 1 16 2015 13 2 4 -18 2015 13 2 1 20 2015 13 2 -8 -6 2015 13 2 -5 -22 2015 13 2 -9 3 2015 13 2 0 2 2015 13 2 -4 -11 2015 13 2 8 0 2015 13 2 -7 -10 2015 13 2 -14 -19 2015 13 2 7 2 2015 13 2 -8 -4 2015 13 2 5 2 2015 13 2 4 4 2015 13 2 8 1 2015 13 2 21 4 2015 13 2 3 6 2015 13 2 11 1 2015 13 2 2 -10 2015 13 2 -23 -12 2015 13 2 0 8 2015 13 2 4 14 2015 13 2 3 11 2015 13 2 2 -14 2015 13 2 0 -9 2015 13 2 -1 7 2015 13 2 -7 2 2015 13 2 5 -19 2015 13 2 3 -18 2015 13 2 8 5 2015 13 2 12 10 2015 13 2 -12 -10 2015 13 2 -15 -6 2015 13 2 -11 -3 2015 13 2 -7 11 2015 13 2 17 14 2015 13 2 -15 -24 2015 13 2 -13 -3 2015 13 2 -17 -3 2015 13 2 -21 -5 2015 13 2 4 0 2015 13 2 -19 -6 2015 13 2 -24 6 2015 13 2 3 0 2015 13 2 0 -8 2015 13 2 4 0 2015 13 2 0 -6 2015 13 2 -2 9 2015 13 2 -8 -9 2015 13 2 -5 -4 2015 13 2 6 12 2015 13 2 5 10 2015 13 2 1 -15 2015 13 2 -12 -7 2015 13 2 -14 3 2015 13 2 7 9 2015 13 2 8 11 2015 13 2 -16 7 2015 13 2 -11 -23 2015 13 2 -17 -24 2015 13 2 -20 -15 2015 13 2 10 9 2015 13 2 4 -25 2015 13 2 -14 -14 2015 13 2 -22 -3 2015 13 2 -22 -4 2015 13 2 -3 -5 2015 13 2 -4 -4 2015 13 2 2 -4 2015 13 2 -4 5 2015 13 2 -2 9 2015 13 2 0 2 2015 13 2 6 1 2015 13 2 -6 4 2015 13 2 2 -5 2015 13 2 -9 -4 2015 13 2 -3 -1 2015 13 2 -10 -7 2015 13 2 -13 -1 2015 13 2 7 0 2015 13 2 -10 -19 2015 13 2 -12 -4 2015 13 2 -13 -3 2015 13 2 -16 -10 2015 13 2 -20 2 2015 13 2 1 -23 2015 13 2 -14 -19 2015 13 2 -21 5 2015 13 2 -17 -17 2015 13 2 3 8 2015 13 2 -1 2 2015 13 2 -1 -3 2015 13 2 0 2 2015 13 2 -2 -1 2015 13 2 -7 1 2015 13 2 -4 -6 2015 13 2 0 5 2015 13 2 11 8 2015 13 2 3 -9 2015 13 2 -11 -5 2015 13 2 -12 -7 2015 13 2 -11 -3 2015 13 2 -8 -2 2015 13 2 -13 -6 2015 13 2 -16 -14 2015 13 2 -16 -12 2015 13 2 7 2 2015 13 2 2 -17 2015 13 2 -21 -15 2015 13 2 3 1 2015 13 2 9 3 2015 13 2 0 -12 2015 13 2 3 18 2015 13 2 0 4 2015 13 2 -5 -20 2015 13 2 -3 -24 2015 13 2 -3 -18 2015 13 2 -3 -4 2015 13 2 -3 -2 2015 13 2 -4 -1 2015 13 2 9 -3 2015 13 2 0 -5 2015 13 2 -8 5 2015 13 2 -10 -5 2015 13 2 12 5 2015 13 2 5 8 2015 13 2 -16 -6 2015 13 2 -16 -2 2015 13 2 -13 0 2015 13 2 -13 -8 2015 13 2 3 10 2015 13 2 -19 6 2015 13 2 0 14 2015 13 2 -20 6 2015 13 2 2 -13 2015 13 2 -3 -20 2015 13 2 -2 -6 2015 13 2 3 5 2015 13 2 5 23 2015 13 2 -1 6 2015 13 2 -8 0 2015 13 2 -3 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-14 -5 2015 13 2 -14 -3 2015 13 2 -17 -1

Matlab

Given an array of monthly rainfall that covers some number of years

(where each column is a month and each row is a year)

create a function YEARLY that prints the average rainfall for each year

For example, if the information below were to be stored in a 5x12 matrix RAIN...

     J F M A M J J A S O N D
2003 1 2 1 2 1 2 1 2 1 2 1 2
2004 1 1 1 1 1 1 1 1 1 1 1 1
2005 2 2 2 2 2 2 2 2 2 2 2 2
2006 1 2 3 1 2 3 1 2 3 1 2 3
2007 5 1 2 4 3 3 5 1 2 4 3 3

Then the function YEARLY(RAIN) would print the result

average rainfall for year 1 is 1.500000
average rainfall for year 2 is 1.000000
average rainfall for year 3 is 2.000000
average rainfall for year 4 is 2.000000
average rainfall for year 5 is 3.000000

Note that only the rain amounts (not the labels) are stored in the input array (RAIN).

: Find the inverse of the three matrices listed below. The code should prompt the user to input the size of the matrix and to put the value of each element in the matrix. The output should contain the solution to the inverse from using a function created by you, and the solution found using the NumPy package.

I1 = [ 1 2 3 4]−1

I2 = [ 1 2 3 4 5 6 7 2 9 ] −1

I3 =[ 1 3 5 9 1 3 1 7 4 3 9 7 5 2 0 9 ] −1

In parts a-d evaluate the following determinants. show all steps.

a. 2x2 matrix the first row being 1 and 2 the second row being -3 and 4.

b. 3x3 matrix, the first row being 2,1, 5, the second row being 0, 3, 2, the third row being 0, 0, 4.

c. 3x3 matrix, the first row being 3, -1, 4, the second row being 2, -2, 3, the third row being 1, -1, 2

d. 4x4 matrix, the first row being 1, 1, 0, 3, the second row being 0, 2, 0, 0, the third row being 0, 3, -2, 1, the fourth row being 0, 4, 3, 2.

e. Which matrices in parts a-d are invertible? how do you know? show all steps.

A company has sales of automobiles in the past three years as given in the table below. Find the seasonal components. (You do not have to find the trend line and apply the seasonal components. This makes this much easier.)

Mr. D works full-time as a systems analyst for a consulting firm. In addition, he sells plants that he raises himself in a greenhouse attached to his residence. During the past 5 years, the results from raising and selling the plants have been as follows: Year Net Profit (Loss) from Scenario 1:

2. Please create a scenario (Scenario 2) where the cumulative profits in years 1-4 are still $300 but the taxpayer would be in a better position regarding year 5 losses.

3. Comment on your answer to 2 above. Why is Scenario 2 better for the taxpayer?

For the fish mortality data set, use an appropriate ANOVA design to determine whether age affects proportional mortality while accounting for variation in mortality due to life history strategy. If age has a significant influence on sunfish mortality, see if you can determine which age results in a different mortality rate.

MORTALITY OF A SUNFISH AFFECTED BY LIFE HISTORY STRATEGY AND AGE

% MORTALITY: 38, 42, 14, 41, 41, 16, 36, 39, 18, 32, 36, 15, 28, 33, 17

LIFE HISTORY STRATEGY: 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5

AGE: 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3