Jeff is willing to invest $6,000 in buying shares and bonds of a company to gain maximum returns. From his past experience, he estimates the relationship between returns and investments made in this company to be:

R = –2S² – 9B² – 4SB + 20S + 30B.        

where,
R = total returns in thousands of dollars
S = thousands of dollars spent on Shares
B = thousands of dollars spent on Bonds
Jeff would like to develop a strategy that will lead to maximum return subject to the restriction provided on the amount available for investment.

a. What is the value of return if $4,000 is invested in shares and $2,000 is invested bonds of the company?
b. Formulate an optimization problem that can be solved to maximize the returns subject to investing no more than $6,000 on both shares and bonds.
c. Determine the optimal amount to invest in shares and bonds of the company. How much return will Jeff gain? Round all your answers to two decimal places.

1. A bank president claims that the median of debt-to-equity ratio of commercial loans provided is less than 5. A random sample of 15 commercial loans is selected with the following values for this ratio:

1.31                 1.33                 1.22

1.78                 1.45                 1.32

1.46                 1.41                 1.19

1.05                 1.29                 1.11

1.37                 1.21                 1.65

Use a Sign Test at the 0.05 level to test this claim. DO THIS BY HAND and not using Excel.

A random sample of 46 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.01 years, with sample standard deviation s = 0.72 years. However, it is thought that the overall population mean age of coyotes is μ = 1.75. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use α = 0.01.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ = 1.75 yr; H₁: μ ≠ 1.75 yrH₀: μ = 1.75 yr; H₁: μ < 1.75 yr    H₀: μ < 1.75 yr; H₁: μ = 1.75 yrH₀: μ > 1.75 yr; H₁: μ = 1.75 yrH₀: μ = 1.75 yr; H₁: μ > 1.75 yr

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since the sample size is large and σ is unknown.The Student's t, since the sample size is large and σ is unknown.    The standard normal, since the sample size is large and σ is known.The Student's t, since the sample size is large and σ is known.

What is the value of the sample test statistic? (Round your answer to three decimal places.)


(c) Find the P-value. (Round your answer to four decimal places.)


Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that coyotes in the specified region tend to live longer than 1.75 years.There is insufficient evidence at the 0.01 level to conclude that coyotes in the specified region tend to live longer than 1.75 years.    

The table below summarizes data from a survey of a sample of women. Using a

0.010.01

significance​ level, and assuming that the sample sizes of

800800

men and

400400

women are​ predetermined, test the claim that the proportions of​ agree/disagree responses are the same for subjects interviewed by men and the subjects interviewed by women. Does it appear that the gender of the interviewer affected the responses of​ women?

Click here to view the chi-square distribution table.

LOADING...

Identify the null and alternative hypotheses. Choose the correct answer below.

A.

Upper H 0H0​:

The response of the subject and the gender of the subject are independent.

Upper H 1H1​:

The response of the subject and the gender of the subject are dependent.

B.

Upper H 0H0​:

The proportions of​ agree/disagree responses are the same for the subjects interviewed by men and the subjects interviewed by women.

Upper H 1H1​:

The proportions are different.

C.

Upper H 0H0​:

The proportions of​ agree/disagree responses are different for the subjects interviewed by men and the subjects interviewed by women.

Upper H 1H1​:

The proportions are the same.

2. what is the test statistic?

3. what is the critical value x squared?

4 fail to reject or reject and why?

Two hundred students are each asked to compute 95% CIs for a population mean based on data they will collect. What is the approximate probability that more than 190 of the CIs will cover the true mean? Please help me understand how to solve this question. The answer is 0.44

Significance vs. meaningfulness:

1. Provide an example of a finding that may be both statistically significant and  meaningful.
2. Provide an example of a finding that may be statistically significant, but not meaningful.

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. The National Council of Small Businesses is interested in the proportion of small businesses that declared Chapter 11 bankruptcy last year. Since there are so many small businesses, the National Council intends to estimate the proportion from a random sample. Let p be the proportion of small businesses that declared Chapter 11 bankruptcy last year. (a) If no preliminary sample is taken to estimate p, how large a sample is necessary to be 98% sure that a point estimate p̂ will be within a distance of 0.10 from p? (Round your answer up to the nearest whole number.) small businesses (b) In a preliminary random sample of 30 small businesses, it was found that ten had declared Chapter 11 bankruptcy. How many more small businesses should be included in the sample to be 98% sure that a point estimate p̂ will be within a distance of 0.100 from p? (Round your answer up to the nearest whole number.) more small businesses

Diagnosis Category

Conduct Tukey's HSD post hoc test to determine where there is a difference in the three groups.

5% level of significance

Write your thoughts on this discussion.

Hypothesis testing is a statistical tool useful for ascertaining information about a specific conclusion. Specifically, this type of testing can help with understanding a data set (population) and the samples of data used to make assertions about those populations. The general process for testing a hypothesis involves selecting a particular element of a population such as the "mean, proportion, standard deviation, or variance" (Evans, p139) and then looking for a contrasting detail to compare with the original supposition or hypothesis. In greater detail, select a hypothesis and one that contrasts with the original (alternate hypothesis), then determine what outcome could occur if the original hypothesis is incorrect. Figure out the criteria for deciding if its true or not. Get data, then apply the that criteria to the data and determine if the hypothesis test results in a positive or negative finding. Parametric Hypothesis testing is a method of testing population data where the data is supposed to fall into a normal distribution. A normal distribution is the "bell-shaped curve." Nonparametric hypothesis testing is done where the data a presumably not a "normal" distribution. In other words will be some other shape that the bell-shaped curve.

1) It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that exactly three of five chosen calculators are defective?

A) 0.00729

B) 0.0081

C) 0.081

D) 0.03

2)For a particular clothing store, a marketing firm finds that 16% of $10-off coupons delivered by mail are redeemed. Suppose six customers are randomly selected and are mailed $10-off coupons. What is the expected number of coupons that will be redeemed?

A) 0.81

B) 0.96

C) 3.42

D) 5.04

3)

The GPA of accounting students in a university is known to be normally distributed. A random sample of 20 accounting students results in a mean of 2.92 and a standard deviation of 0.16. Construct the 95% confidence interval for the mean GPA of all accounting students at this university.

A) 2.92 ± 1.729(0.16/ )

B) 2.92 ± 1.96(0.16/ )

C) 2.92 ± 2.086(0.16/ )

D) 2.92 ± 2.093(0.16/ )

4)

The probability that a normal random variable is less than its mean is ________.

A) 0.0

B) 0.5

C) 1.0

D) Cannot be determined

5)

A company that produces computers recently tested the battery in its latest laptop in six separate trials. The battery lasted 8.23,7.89,8.14,8.25,8.30, and 7.95 hours before burning out in each of the tests. Assuming the battery duration is normally distributed, construct a 95% confidence interval for the mean battery life in the new model.

A) [7.9490, 8.3044]

B) [7.9575, 8.2959]

C) [7.9873, 8.2661]

D) [7.9912, 8.2622]

A researcher is studying memory for different types of words under low, and high memory load. She uses concrete words (e.g., dog, boat) and abstract words (e.g. love, height) in a factorial design, with five participants in each cell. With part of the information in the summary table, please finish the table and conduct the analysis.

a. Test and draw conclusions about the main effect of memory load.

b. Test and draw conclusions about the main effect of word type.                                 

c. Test and draw conclusions about the memory load x word type interaction

1. A Toyota dealer consumes four kinds of engine oil A, B, C and D. This dealer buys its consumption each week. The dealer never buys the same brand in successive weeks, except brand D. If the dealer buys engine oil D then with same probability it can buy all kinds of engine oils next week. If the dealer perches brand C then next week it will buy D. However, if the dealer buys engine oil B then the next week it is four times as likely to perches A as the other brands and finally if the dealer buy engine oil A it will buy D or C with same probabilities. What is the probability that mentioned dealer buys oil C when we know that oil B was purchased three weeks ago?

discrete probability distributions

There are 37 different processors on the motherboard of a controller. 6 of the processors are faulty. It is known that there are one or more faults on the motherboard. In an attempt to locate the error, 7 random processors are selected for testing.

tasks

a) Determine the expected number of defective processors. Round your answer to 2 decimal places.

b) Determine the variance of the number of defective processors. Round your answer to 4 decimal places.

c) Determine the standard deviation of the number of defective processors. Round your answer to 2 decimal places.

d) What is the probability that there are at least 2 faulty processors? Round your answer to 4 decimal places.

e) What is the probability that there are exactly 1 faulty processors if there are a maximum of 2 faulty processors?  Round your answer to 4 decimal places.

discrete probability distributions

Pernilles Super'Chip is a processor for super-fast image analysis. It is put into production in a factory. In this factory it turns out that the probability of a Super'Chip being defective is 2%. Consider the next 17 independent Super'Chips being produced.

tasks

a) Determine the expected number of defective Super'Chip. (Round your answer to 2 decimal places. )

b)  Determine the variance of the number of defective Super'Chip (Round your answer to 4 decimal places. )

c) Determine the standard deviation of the number of defective Super'Chip. (Round your answer to 2 decimal places. )

d) What is the probability that there is a maximum of 2 defective Super'Chip?  (Round your answer to 4 decimal places. )

e) What is the probability that there are exactly 8 Super'Chip if there are at least 2 defective Super'Chip? (Round your answer to 4 decimal places. )

A marketing research professor is conducting a telephone survey and needs to contact at least 160 wives, 140 husbands, 110 single adult males, and 120 single adult females. It costs $2 to make a daytime call and $4 (because of higher labor costs) to make an evening call. The table shown below lists the expected results. For example, 10% of all daytime calls are answered by a single male, and 15% of all evening calls are answered by a single female. Because of a limited staff, at most half of all phone calls can be evening calls. Determine how to minimize the cost of completing the survey

Develop a Report for the following

3) Find the optimal solution. State the call plan and total cost.