|
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
In: Math
It is well established that both nature (genetics) and nurture (environment) play a role in who we are and how we behave as humans. One way to examine the effect of nature vs. nurture is to study children who have been adopted at birth. These children are unique in that they received genes from their birth parents and have environmental influence from their adoptive parents. For example, a research study can be conducted to see if the Body Mass Index (BMI) is more correlated with the BMI of his/her birth parent or adoptive parent. If the BMI of the child is more correlated with the birth parent’s BMI, it means that the weight might be genetically determined to a larger extent compared to environmental influence. If it’s more correlated with the adoptive parent’s BMI, then it means that the weight might be influenced by the behavior of the adoptive parent to a larger extent.
Use the following dataset to answer the questions below:
BMI |
|||
Subject ID # |
Child |
Child’s Birth Parent |
Child’s Adoptive Parent |
1 |
22 |
26 |
20 |
2 |
21 |
17 |
22 |
3 |
25 |
23 |
22 |
4 |
19 |
25 |
21 |
5 |
20 |
19 |
25 |
6 |
17 |
19 |
17 |
7 |
25 |
21 |
27 |
8 |
18 |
19 |
17 |
9 |
20 |
28 |
23 |
10 |
19 |
23 |
21 |
Questions:
In: Math
*****Show step-by-step in Excel******
An automobile rental company wants to predict the yearly maintenance expense (Y) for an automobile using the number of miles driven during the year ( X1 ) and the age of the car ( X2 , in years) at the beginning of the year. The company has gathered the data on 10 automobiles and the regression information from Excel is presented below. Use this information to answer the following questions.
Summary measures Multiple R 0.9689 R-Square 0.9387 Adj R-Squared 0.9212 StErr of Estimate 72.218
Regression Coefficient | ||||
Coefficient | std err | t-value | p-value | |
constant | 33.796 | 48.181 | 0.7014 | 0.5057 |
Miles Driven | 0.0549 | 0.0191 | 2.8666 | 0.0241 |
Age of Car | 21.467 | 20.573 | 1.0434 | 0.3314 |
a. Use the information above to write out the estimated linear regression model.
b. Interpret each of the estimated coefficients of the regression model in part (a).
c. Identify and interpret the coefficient of determination ( R2 ) and the adjusted R2 .
d. Does the given set of explanatory variables do a good job of explaining changes in the maintenance costs? Explain why or why not.
In: Math
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 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.)
|
In: Math
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 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
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 |
In: Math
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 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 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 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?”
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
How do the findings fail to reject or reject the null hypothesis?
In: Math
In: Math
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