Questions are below

kenneth brown is the principal owner of brown oil inc. After quitting his university teaching job. ken has been able to increase this annual salary by a factor of over 100. at the present time, ken is forced to consider purchasing some more equipment for brown oil because of competition. his alternatives are shown in the following table

equipment favorable market ($) unfavorable market ($)

sub 100 300,000 - 200,000

oiler J 250,000 - 100,000

texan 75,000 -18,000

for example, if ken purchases a sub 100 and if there is a favorable market, he will realize a profit of $300,000. On the other hand, if the market is unfavorable. ken will suffer a loss of $200.000. But ken has always been a very optimistic decision maker.

(a) what type of decision is ken facing?

(b) what decision criterion should be use?

(c) what alterntive is best?

The probability of a student playing football is known to be 0.53; and the probability of a student playing rugby is known to be 0.5. If the probability of playing both is known to be 0.38, calculate:

(a) the probability of playing rugby

(b) the probability of playing at least one of football and rugby

(c) the probability of a student playing rugby, given that they play football

(d) Are playing rugby and football independent? Justify

(e) (harder) a group of 29 randomly selected students attend a special seminar on the health benefits of playing sport. Of these 29, only 5 play neither after the seminar. State a sensible null hypothesis, test it, and interpret.

Notes:

Show detailed working, including appropriate mathematical notation for each question. For most questions this will involve showing your working from R Studio, (e.g. cut-and-paste commands and output from an R session).

Any question involving regression will score 0 marks unless a scattergraph is produced.

No Additional Info provided

1.) A statistics practitioner took a random sample of 42 observations from a population whose standard deviation is 21 and computed the sample mean to be 103. Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits.

A. Estimate the population mean with 95% confidence.

Confidence Interval =

B. Estimate the population mean with 95% confidence, changing the population standard deviation to 57;

Confidence Interval =

C. Estimate the population mean with 95% confidence, changing the population standard deviation to 12;

Confidence Interval =

----------------------------

2.) The number of cars sold annually by used car salespeople is normally distributed with a standard deviation of 17. A random sample of 430 salespeople was taken and the mean number of cars sold annually was found to be 69. Find the 96% confidence interval estimate of the population mean.

Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits.

Confidence Interval =

--------

3.)

A random sample of 13 size AA batteries for toys yield a mean of 2.78 hours with standard deviation, 0.63 hours.

(a) Find the critical value, t*, for a 99% CI. t* =

(b) Find the margin of error for a 99% CI.

PLEASE USE R STUDIO AND NOT INVOLVE REGRESSION

In NZ supermarkets, the average weight of a banana is 118.6 grams. An agricultural scientist buys bananas from a supermarket. Their weight, in grams, is as follows: c(108.4, 125.9, 96.1, 136.6, 109.3, 116.4, 88.6, 79, 88) She suspects that this sample of bananas is lighter than average and wonders if this supermarket is selling bananas that are lighter than the NZ average.

(a) State a sensible null hypothesis

(b) State the precise definition of p-value and explain what "more extreme" means in this context

(c) Is a one-sided or two-sided test needed? justify

(d) Perform a student t-test using R and interpret

(e) Perform a Z test and account for any differences you find

PLEASE USE R STUDIO AND NOT INVOLVE REGRESSION

Question 1

Which one of the following methods can NOT be used for a numeric response variable?

Group of answer choices

Random Forest

Regression Tree

K nearest Neighbor

Classification Tree

Question 2

Given data, we get the following result for a logistic regression ln ( o d d s r a t i o ) = 2 x 1. what is the estimate of p (probability of success) at point x=0.10415

Group of answer choices

-0.7917

0.31

3.20

0.28

Consider the following problem. We want to n regression tree (with one split) on the NEG variable to predict the average GDP in each region (R1 and R2). The no split model is represented in the left graph.

Assume by one split at NEG <-10 vs NEG -10 we get the following fit mean output for each region. (The two graphs on the right)

Answer the following three questions.

Question 3

Calculate the R-sq of the NO SPLIT model

Group of answer choices

0.83

0

317.4083

1

Question 4

What is the amount of SSE of the one split model?

Group of answer choices

11.77819

114.51899

0

102.7408

Question 5

Calculate the SSE reduction based on the one split.

Group of answer choices

0

202.88931

114.51899

317.4083

Question 6

Calculate the R-sq of the one split model.

Group of answer choices

0

0.3608

0.6392

0.0371

Question 7

Given the following confusion matrix, Calculate the False Negative and True Negative rates respectively.

Group of answer choices

0.384,0.317

0.383,0.683

0.683,0.383

0.317,0.384

Question 8

Which of the following is TRUE?

Group of answer choices

Random Forest only chooses a random subset of variables to split on in each leaf node.

In JMP decision tree, when we have multiple predictors, we split on the variable with the smallest candidate SSE.

Each time wen random forest we get the same training R-sq value.

Both the Validation and Training R-sq will go up by each split added to the model because it creates a more accurate prediction.

Question 9

Given some operational conditions as predictor variables, we intend to predict if a machine is failed or not failed. Which of the following methods is not appropriate?

Group of answer choices

Classification Tree

Regression Tree

Random Forest

Logistic Regression

Question 10

120 out of 600 patients reported having allergies to a drug. What is the odds of NOT being allergic?

Group of answer choices

0.2

0.25

0.8

4

Question 11

Which one of the following statements is TRUE.

Group of answer choices

Trees are parametric methods because they consider a functional form for the prediction.

Trees are very flexible to fit not well behaving response variables.

Trees split on the response variable range and each leaf will cover only a certain range of the response variable.

Trees can only be used with continuous predictor variables.

Question 12

Given the following ROC curve, which model one is the worst model?

Group of answer choices

Test 1

Test 3

Test 2

Question 13

Consider the following regression tree. what is the prediction of the response variable when L T G 4.6052 and 24.4 < B M I < 27.8.

Group of answer choices

176.86486

159.743

74

208.57143

Question 14

Suppose quarterly sales was fitted with a seasonal model of 5*Q4+375 where Q4 is an indicator variable for the fourth quarter. What is the predicted sales for the second quarter?

Group of answer choices

0

5

375

380

Question 15

Suppose the best fitting model for a time series is y(t) = 12.4+0.25y(t-1). Suppose the observation values for the first 10 periods (read left to right) are 13,15,19,16,18,15,13,14,17,19

What is the prediction for period 12?

Group of answer choices

19

16.6875

15.9

17.15

Question 16

Which of the following is NOT true?

Group of answer choices

All regressions (time series and non-time series applications) should be followed up with an ACF on the residuals.

For a given time series, the PACF and ACF at lag 1 are equal.

For a given time series, the PACF and ACF at lag 1 are equal.

PACF is the correlation of a time series with its lags removing the effects of intervening lags.

Question 17

ACF cannot be used for determining what lags can serve as predictor variables in the regression model.

Group of answer choices

True

False

Question 18

Which one of the following models is an AR(2) model.

Group of answer choices

y(t) = b0 + b1*y(t-1)

y(t) = b0 + b1*t+b1*t squared

y(t) = b0 + b1*y(t-1)+b2* y(t-2)

y(t) = b0 + b1*t

Consider two different stocks, X and Y, with expected returns mX = 17.0% and mY = 14.9% and with standard deviations sX = 12.4% and sY = 10.0% for those returns. The two assets have a correlation, pr, of -0.7.

a. What is the covariance of the returns of stocks X and Y? (Hint: use the definition of the population correlation r to compute the covariance) In general, will constructing a portfolio from these two stocks reduce or increase the risk compared to the individual stocks? Briefly explain.

b. What is the expected return and standard deviation of a portfolio made up of stocks X and Y which is 20% stock X (the remainder stock Y)?

c. What is the expected return and standard deviation of a portfolio made up of stocks X and Y which is 50% stock X?

d. What is the expected return and standard deviation of a portfolio made up of stocks X and Y which is 80% stock X? e. Which of the portfolios above, either (b), (c), or (d), offers the best combination of risk and return? Briefly explain.