The following regression output was obtained from a study of architectural firms. The dependent variable is the total amount of fees in millions of dollars.
Predictor 
Coef 
SE Coef 
T 
P 

Constant 
7.987 
2.967 
2.69 
 

X1 
0.12242 
0.03121 
3.92 
0.0000 

X2 
0.12166 
0.05353 
2.27 
0.028 

X3 
0.06281 
0.03901 
1.61 
0.114 

X4 
0.5235 
0.1420 
3.69 
0.001 

X5 
0.06472 
0.03999 
1.62 
0.112 

Analysis of Variance 

Source 
DF 
SS 
MS 
F 
P 
Regression 
5 
3710.00 
742.00 
12.89 
0.000 
Residual Error 
46 
2647.38 
57.55 

Total 
51 
6357.38 
X1  # of architects employed by the company
X2  # of engineers employed by the company
X3  # of years involved with health care projects
X4  # of states in which the firm operates
X5  % of the firms work that is health carerelated
In: Math
Use R to complete the following questions. You should include your R code, output and plots in your answer.
1. Two methods of generating a standard normal random variable are:
a. Take the sum of 5 uniform (0,1) random numbers and scale to have mean 0 and standard deviation 1. (Use the properties of the uniform distribution to determine the required transformation).
b. Generate a standard uniform and then apply inverse cdf function to obtain a normal random variate (Hint: use qnorm).
For each method generate 10,000 random numbers and check the distribution using
a. Normal probability plot
b. Mean and standard deviation
c. The proportion of the data lying within the theoretical 2.5 and 97.5 percentiles and the 0.5 and 99.5 percentiles. (Hint: The ifelse function will be useful)
In: Math
If the probability that a family will buy a vacation home in Manmi, Malibu, or Newport is 0.25, 0.10, 0.35, what is the probability the family will consummate one of these transactions? please show all wor with explanation.
In: Math
In the following problem, check that it is appropriate to use
the normal approximation to the binomial. Then use the normal
distribution to estimate the requested probabilities.
What are the chances that a person who is murdered actually knew
the murderer? The answer to this question explains why a lot of
police detective work begins with relatives and friends of the
victim! About 68% of people who are murdered
actually knew the person who committed the murder.† Suppose that a
detective file in New Orleans has 65 current
unsolved murders. Find the following probabilities. (Round your
answers to four decimal places.)
(a) at least 35 of the victims knew their murderers
(b) at most 48 of the victims knew their murderers
(c) fewer than 30 victims did not know their murderers
(d) more than 20 victims did not know their murderers
In: Math
Mr. James McWhinney, president of DanielJames Financial Services, believes there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, Mr. McWhinney gathered the following sample information. The X column indicates the number of client contacts last month, and the Y column shows the value of sales ($ thousands) last month for each client sampled.
Number of Contacts (X) 
Sales ($ thousands) (Y) 
14 
24 
12 
14 
20 
28 
16 
30 
46 
80 
23 
30 
48 
90 
50 
85 
55 
120 
50 
110 
In: Math
Professor Nord stated that the mean score on the final exam from all the years he has been teaching is a 79%. Colby was in his most recent class, and his class’s mean score on the final exam was 82%. Colby decided to run a hypothesis test to determine if the mean score of his class was significantly greater than the mean score of the population. α = .01. If p = 0.29
What is the mean score of the population? What is the mean score of the sample? What should Colby’s statement of conclusion be
In: Math
(20.37) Researchers claim that women speak significantly more words per day than men. One estimate is that a woman uses about 20,000 words per day while a man uses about 7,000. To investigate such claims, one study used a special device to record the conversations of male and female university students over a four day period. From these recordings, the daily word count of the 20 men in the study was determined. Here are their daily word counts:
What value we should remove from observation for applying t procedures? A 90% confidence interval (±±10) for the mean number of words per day of men at this university is from to words. Is there evidence at the 10% level that the mean number of words per day of men at this university differs from 7000?

In: Math
You started taking the bus to work. The local transit authority says that a bus should arrive at your bus stop every five minutes. After a while, you notice you spend a lot more than five minutes waiting for the bus, so you start to keep a record.
You spend the next two months recording how long it takes for the bus to arrive to the bus stop. This give a total of sixty observations that denote the number of minutes it took for the bus to arrive (rounded to the nearest minute). These observations are hosted at
https://mattbutner.github.io/data/bus_stop_time.csv
Load these data into R as a data frame titled bus_stop_time
Create a histogram of the time_until_bus varaible. Would you say that five minutes is a reasonable guess for the average arrival time based on this picture alone?
Create 95% confidence interval for the bus arrival times using the Z distribution. Does 5 minutes fall within the 95% confidence interval?
How would you communicate your finding to the local transit authority?
In: Math
In: Math
For this problem, carry at least four digits after the decimal
in your calculations. Answers may vary slightly due to
rounding.
In a random sample of 63 professional actors, it was found that 39
were extroverts.
(a) Let p represent the proportion of all actors who
are extroverts. Find a point estimate for p. (Round your
answer to four decimal places.)
(b) Find a 95% confidence interval for p. (Round your
answers to two decimal places.)
lower limit  
upper limit 
Give a brief interpretation of the meaning of the confidence
interval you have found.
We are 5% confident that the true proportion of actors who are extroverts falls within this interval.We are 95% confident that the true proportion of actors who are extroverts falls outside this interval. We are 5% confident that the true proportion of actors who are extroverts falls above this interval.We are 95% confident that the true proportion of actors who are extroverts falls within this interval.
(c) Do you think the conditions np > 5 and nq
> 5 are satisfied in this problem? Explain why this would be an
important consideration.
Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal. Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.
In: Math
A study examined whether or not noses continue to grow throughout a person’s lifetime. The study included many measurements (including size of the nose as measured by total volume) and included multiple tests. For each of the tests described below:
a) State the null and alternative hypotheses.
b) Give a formal decision using a 5% significance level, and interpret the conclusion in context.
In: Math
The failure rate in a statistics class is 20%. In a class of 30 students, find the probability that exactly five students will fail. Use the normal distribution to approximate the binomial distribution.
In: Math
The mean number of pets per household is 2.96 with standard deviation 1.4. A sample of 52 households is drawn. Find the probability that the sample mean is less than 3.11.
a. 
0.2245 

b. 
0.5676 

c. 0.3254 

d. 
0.7726 
In: Math
The pH of 20 randomly selected lakes is measured. Their average pH is 5.7.
Part A. Historically the standard deviation in the pH values is
0.9. Use this standard deviation for the following questions.
Part Ai. Build a 95% confidence interval for the population mean
lake pH.
Part Aii. Build a 90% confidence interval for the population mean
lake pH.
Part Aiii. Build an 80% confidence interval for the population mean
lake pH.
Part Aiv. Compare the intervals you created in Ai, Aii and Aiii.
What effect does changing the level of confidence have on the
interval?
Please solve only part B
Part B. For the 20 measured lakes the standard deviation in the
pH values is 0.9. Use this standard deviation for the following
questions.
Part Bi. Build a 95% confidence interval for the population mean
lake pH.
Part Bii. Compare the confidence intervals in Bi and Ai. What
effect does not knowing the value of ? have on the interval?
Part Biii. Test whether the population mean pH differs from 6.
In: Math
For 300 trading days, the daily closing price of a stock (in $) is well modeled by a Normal model with a mean of
$197.12197.12 and a standard deviation of
$7.187.18. According to this model, what is the probability that on a randomly selected day in this period, the stock price closed as follows.
a) above $204.30204.30?
b) below $211.48211.48?
c) between $182.76182.76 and $211.48211.48?
In: Math