Questions
In this exercise you are choosing between the following investment strategies: Invest $200 in stock A....

In this exercise you are choosing between the following investment strategies:

Invest $200 in stock A. Stock A costs $20 per share. Expected yield per share of stock A is $2, and the variance of yield per share is 9 ($-squared).

Invest $200 in stock B. Stock B costs $10 per share. Expected yield per share of stock B is $0.90, and the variance of yield per share is 1 ($-squared).

Invest $100 in stock A and $100 in stock B. The correlation between yield per share of stock A and yield per share of stock B is 0.12.

1)With strategy (iii), how many shares of stock A and stock B do you buy?

a) 10 shares of A and 20 shares of B

b) 5 shares of A and 10 shares of B

c)10 of each

d) 20 of each

2)What is the value of the covariance between the yield on a share of stock A and the yield on a share of stock B?

a) 0.16

b)0.12

c) 1.08

d) 0.36

3) When will portfolio (iii) lose money?

a) When the yield on portfolio (iii) is less than the expected yield on portfolio (iii)

b) When the yield on portfolio (iii) is negative

c) When the yield on stock A is negative and the yield on stock B is negative

d)When the yield on stock A is negative or the yield on stock B is negative

In: Math

A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of...

A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. Her realtor friend informs them that the last 28 houses that sold in their neighborhood took an average time of 220 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 40 days. [You may find it useful to reference the z table.]

b. Construct the 95% confidence interval for the mean sale time for all homes in the neighborhood. (Round intermediate calculations to at least 4 decimal places. Round "z" value to 3 decimal places and final answers to 2 decimal places.)

Confidence interval to

In: Math

The distribution of durations for which apartments remain empty after the resident moves out for one...

The distribution of durations for which apartments remain empty after the resident moves out for one property management company over the past 10 years was approximatley normal with mean of 95 days and a standard deviation of 29 days. The property management company intends to update the kitchen appliances in the apartments that were empty for top 10% of durations. What is the minimum duration for which an apartment remained empty for the company to update the kitchen appliances? Round to the nearest whole number.
Choose 1 answer:
A) 48 days
B) 112 days
C) 114 days
D) 123 days
E) 129 days

In: Math

This is a two part question: a) How will the company benefit from implementing Design for...

This is a two part question:

a) How will the company benefit from implementing Design for Reliability (DFR)

program? Names four of such benefits.

b) What are some of the critical inputs to Design FMEA/FMECA? Please name four

and very briefly discuss.

In: Math

You are a nursing researcher and you are interested in whether university grades are predictive of...

  1. You are a nursing researcher and you are interested in whether university grades are predictive of performance on the NCLEX exam. You randomly select a sample of 25 nurses from the Ontario registry and obtain each nurse’s score on the NCLEX examination. You also have access to their final grade in university. The complete data are shown in the table below. Use these data to answer the questions below the table. Assume a 0.05 level of significance.

Nurse

NCLEX Score

Final Grade (University)

1

440

87

2

480

87

3

535

87

4

460

88

5

525

88

6

480

89

7

510

89

8

530

89

9

545

89

10

600

89

11

495

90

12

545

90

13

575

90

14

525

91

15

575

91

16

600

91

17

490

92

18

510

92

19

575

92

20

540

93

21

595

93

22

525

94

23

545

94

24

600

94

25

625

94

  1. Use SPSS to obtain the predictive equation. Provide the equation and the supporting SPSS output. [1 Mark]

  1. Use an appropriate statistic provided by the SPSS output to describe the utility (goodness) of the regression equation for predicting NCLEX scores. [1 Mark]
  1. What is the predicted NCLEX score for a final grade = 75? [1 Mark]
  1. What is the unexplained variation in NCLEX scores for your regression model? Show your calculation. [1 Mark]

In: Math

A research service estimates that the mean annual consumption of fresh market tomatoes by a person...

A research service estimates that the mean annual consumption of fresh market tomatoes by a person in the US is atleast 21 pounds. You doubt this claim. A simple random sample of 23 people in the US has a mean annual consumption of fresh market tomatoes of Xbar=19 pounds and a standard deviation of 4 pounds. Assume the pop. is normally distributed. Construct the appropriate hypothesis and conduct the test at the 1% level of significance. Based on the Critical Value approach is there enough evidence to reject the claim?

In: Math

A nutrition lab tested 40 randomly selected hot dogs to see if their mean sodium content...

A nutrition lab tested 40 randomly selected hot dogs to see if their mean sodium content was less than 325mg upper limit set by regulations for "reduced sodium" franks. The sample yielded a mean of 322 mg with a standard deviation of 11.5 mg.

A) To construct a confidence interval, would you use a z-chart or a t-chart? why?

B) Construct a 90% confidence interval for for estimating the mean sodium content for "reduced sodium" hot dogs. Interpret the confidence interval in a sentence.

C) Test the claim that the mean sodium level for the "reduced sodium" hot dogs is less than the limit of 325mg. Use a significance level of 0.05.

D) Does the confidence interval support the conclusion of the hypothesis test? Explain.

In: Math

The density of an oil mixture (mix) as a function of the temperature (T) and the...

The density of an oil mixture (mix) as a function of the temperature (T) and the mass fraction of the three components (mi) was measured and results are shown :

T (K) m1 m2 m3 Pmix (kg/m3 )

300 0 1 0 879.6

320 0 0.5 0.5 870.6

340 0 0 1 863.6

360 0.5 0 0.5 846.4

380 0.5 0.25 0.25 830.8

400 0.5 0.5 0 819.1

420 1 0 0 796

440 1 0 0 778.2

Find the coefficients for a multiple regression of the form Pmix = a0 + a1*T + a2*m1 + a3*m2 + a4*m3

In: Math

Researchers conducting a clinical trial randomly assigned 60 patients with painful knee osteoarthritis evenly into one...

Researchers conducting a clinical trial randomly assigned 60 patients with painful knee osteoarthritis evenly into one of three treatment groups: glucosamine, chondroitin, or placebo.After the study period, patients were asked if they experienced substantial improvement in pain and ability to function normally.Thirty-four patients replied that they did have an improvement, including 13 in the glucosamine group, 16 in the chondroitin group, and 5 in the placebo group.

List a potential confounding variable for this study and briefly explain a possible consequence it could have on the results.

In: Math

Topic: “Is there a different between teacher’s and parents’ perceptions of what constitutes effective school-to-home communication?”...

Topic: “Is there a different between teacher’s and parents’ perceptions of what constitutes effective school-to-home communication?”

Ho: this is the currently accepted statement that there is no significant difference between teachers and parents’ perceptions of what constitutes effective school-to home communication.

Ha: this is my research hypothesis that is making the statement that there is a significant difference between teacher’s and parents’ perceptions of what constitutes effective school-to-home communication.

Ho & Ha are opposite mathematically, thus the possible outcomes of this investigation is to

  1. Reject the null hypothesis
  2. Fail to reject the null hypothesis

How do the findings fail to reject or reject the null hypothesis?

  1. Test Statistic- to calculate from sample data
  2. Statistically Significant- making a decision
  3. Level of Confidence- C- 95% , 99%


In: Math

In your own words, describe what you have learned about hypothesis testing and hypothesis testing for...

In your own words, describe what you have learned about hypothesis testing and hypothesis testing for the mean. Give one or more examples of how you could use this information to test a problem. Be specific on what the problem would be about.

In: Math

We have three light bulbs with lifetimes T1,T2,T3 distributed according to Exponential(λ1), Exponential(λ2), Exponential(λ3). In other...

We have three light bulbs with lifetimes T1,T2,T3 distributed according to Exponential(λ1), Exponential(λ2), Exponential(λ3). In other word, for example bulb #1 will break at a random time T1, where the distribution of this time T1 is Exponential(λ1). The three bulbs break independently of each other. The three light bulbs are arranged in series, one after the other, along a circuit—this means that as soon as one or more light bulbs fail, the circuit will break. Let T be the lifetime of the circuit—that is, the time until the circuit breaks.

(a) What is the CDF of T, the lifetime of the circuit?

(b) Next, suppose that we only check on the circuit once every second (assume the times T1,T2,T3,T are measured in seconds). Let S be the first time we check the circuit and see that it’s broken. For example, if the circuit breaks after 3.55 seconds, we will only observe this when 4 seconds have passed, and so S = 4. Calculate the PMF of S.

(c) Finally, suppose that instead of checking on the circuit every second, we instead do the following: after each second, we randomly decide whether to check on the circuit or not. With probability p we check, and with probability 1−p we do not check. This decision is made independently at each time. Now let N be the number of times we check and see the circuit working. For example, if the circuit breaks at time 3.55, and our choices were to check at time 1 second, not to check at times 2 or 3 or 4, and to check at time 5, then N = 1, since the circuit was broken the 2nd time we checked. What is the PMF of N? (Hint: start by finding the joint PMF of N and S. It’s fine if your answer is in summation form.)

In: Math

A nutritionist is interested in the relationship between cholesterol and diet. The nutritionist developed a non-vegetarian...

A nutritionist is interested in the relationship between cholesterol and diet. The nutritionist developed a non-vegetarian and vegetarian diet to reduce cholesterol levels. The nutritionist then obtained a sample of clients for which half are told to eat the new non-vegetarian diet and the other half to eat the vegetarian diet for three months. The nutritionist hypothesizes that the non-vegetarian diet will reduce cholesterol levels more. What can the nutritionist conclude with α = 0.01. Below are the cholesterol levels of all the participants after three months.

non-
vegetarian

vegetarian
117
171
196
211
231
256
131
196
106
121
141
146
156
196
106
106


a) What is the appropriate test statistic?
---Select--- na z-test One-Sample t-test Independent-Samples t-test Related-Samples t-test

b)
Condition 1:
---Select--- cholesterol level non-vegetarian months diet vegetarian
Condition 2:
---Select--- cholesterol level non-vegetarian months diet vegetarian

c) Compute the appropriate test statistic(s) to make a decision about H0.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[  ,  ]

e) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d =  ;  ---Select--- na trivial effect small effect medium effect large effect
r2 =  ;  ---Select--- na trivial effect small effect medium effect large effect

f) Make an interpretation based on the results.

Non-vegetarians had significantly higher cholesterol levels than vegetarians.

Non-vegetarians had significantly lower cholesterol levels than vegetarians.    

There was no significant cholesterol difference between non-vegetarians and vegetarians.

In: Math

Prove "The Birthday Problem" in this regard, Suppose there are some number of people in a...

Prove "The Birthday Problem" in this regard,

Suppose there are some number of people in a room and we need need to consider all possible pairwise combinations of those people to compare their birthdays and look for matches.Prove the probability of the matches.

In: Math

In this problem, we use your critical values table to explore the significance of r based...

In this problem, we use your critical values table to explore the significance of r based on different sample sizes. (a) Is a sample correlation coefficient ρ = 0.82 significant at the α = 0.01 level based on a sample size of n = 3 data pairs? What about n = 14 data pairs? (Select all that apply.) No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 14 and α = 0.01. No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 3 and α = 0.01. Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 3 and α = 0.01. Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 3 and α = 0.01. Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 14 and α = 0.01. No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 3 and α = 0.01. Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 14 and α = 0.01. No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 14 and α = 0.01. Incorrect: Your answer is incorrect. (b) Is a sample correlation coefficient ρ = 0.42 significant at the α = 0.05 level based on a sample size of n = 18 data pairs? What about n = 26 data pairs? (Select all that apply.) Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 26 and α = 0.05. No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 18 and α = 0.05. Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 18 and α = 0.05. Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 26 and α = 0.05. No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 26 and α = 0.05. Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 18 and α = 0.05. No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 18 and α = 0.05. No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 26 and α = 0.05. Incorrect: Your answer is incorrect. (c) Is it true that in order to be significant, a ρ value must be larger than 0.90? larger than 0.70? larger than 0.50? What does sample size have to do with the significance of ρ? Explain your answer. No, a larger sample size means that a smaller absolute value of the correlation coefficient might be significant. No, sample size has no bearing on whether or not the correlation coefficient might be significant. Yes, a larger correlation coefficient of 0.70 means that the data will be significant. Yes, a larger correlation coefficient of 0.90 means that the data will be significant. Yes, a larger correlation coefficient of 0.50 means that the data will be significant.

In: Math