Before opening the dataset needed for this problem, you’ll need to call the “car” package:
> library(car)
Now you can import the “Wong” dataset and use it to answer the question below.
Remember to include any code you use along with your answers in your submission!
3. The Wong dataset contains data from a study by Wong, Monette,
and Weiner (2001) on patients who fell into comas after sustaining
traumatic brain injuries. After waking, Wong and colleagues
administered two different intelligence tests (the “piq” and “viq”
variables). The “duration” variable indicates how long each patient
was in a coma before waking (measured in days).
a. Consider that this dataset represents the population of all
patients who fell into comasafter sustaining traumatic brain
injuries. Calculate the population mean and standard deviation of
the duration variable.
b. Simulate drawing 1,000 random samples of size n =30 and store
the sample mean durations in a vector (see the Lab 4 handout and/or
video). Create a histogram of your sampling distribution of means
for duration.
c. Calculate the mean and standard deviation of your sampling
distribution. How do they compare to the population mean and
standard deviation?
d. If you decreased your sample size to n=10, how would the shape
of your sampling distribution change compared to what you reported
above?
In: Math
Commute times in the U.S. are heavily skewed to the right. We select a random sample of 230 people from the 2000 U.S. Census who reported a non-zero commute time.
In this sample the mean commute time is 28.6 minutes with a standard deviation of 19.3 minutes. Can we conclude from this data that the mean commute time in the U.S. is less than half an hour? Conduct a hypothesis test at the 5% level of significance.
What is the $p$-value for this hypothesis test?
Your answer should be rounded to 4 decimal places
In: Math
The American Bankers Association reported that, in a sample of 125 consumer purchases in France, 62 were made with cash, compared with 21 in a sample of 40 consumer purchases in the United States.
Construct a 99 percent confidence interval for the difference in proportions. (Round your intermediate value and final answers to 4 decimal places.)
The 99 percent confidence interval is from _____ to _____ .
In: Math
Gallup recently conducted a survey about the proportion of Americans who use e-cigarettes (vape). The survey data was collected via random-digit-dial telephone interviews conducted July 1-12, 2019 with a random sample of 1525 adults living in all 50 U.S. states with a minimum quota of 70% cellphone respondents and 30% landline respondents, with additional minimum quotas by time zone within region. The following table summarizes their results for men and women: Men Women Total Vape 92 31 123 Do Not Vape 924 478 1402 Total 1016 509 1525 Problem 2. Does the data suggest that a greater proportion of men vape compared to women? Conduct a hypothesis test to at the 5% significance level by completing the following steps: State the null and alternative hypotheses. Be sure to include proper statistical notation. Check the conditions for inference. Compute the test statistic. For full credit, be sure to show your work. Determine the p-value or the critical value (depending on the method you prefer). Either way, be sure to show your work by drawing a sketch. Using either the p-value or critical value method, make a decision about the null hypothesis. Be sure to show how your decision was made. Based on the results of the hypothesis test, does it appear that “use of e-cigarettes” and “gender” are independent variables? In other words, is it equally likely for a man to vape as it is for a woman to vape? Explain. Would the results of the hypothesis test change at the 1% significance level? Explain.
In: Math
A hand of 13 cards is dealt from a standard deck of 52 playing cards. What is the probability that it contains more spades (♠) than hearts (♡) given that the hand contains at least two spades?
In: Math
A cola-dispensing machine is set to dispense 8 ounces of cola per cup, with a standard deviation of 1.0 ounce. The manufacturer of the machine would like to set the control limit in such a way that, for samples of 34, 5% of the sample means will be greater than the upper control limit, and 5% of the sample means will be less than the lower control limit.
In: Math
Applications of Statistical Process Control and Quality Improvement Tools in Transactional and
Service Business.
The tools are:
1. Cause and Effect Analysis.
2. Check sheets/ tally sheets.
3. Graphs.
4. Histograms.
5. Pareto analysis.
6. Scatter analysis.
7. Control charts.
. For discussion, I want you to discuss how these tools are being used in your realm of work? If they are not
being used, then how do you see them being used? Identify at least one tool being used and explain
how it is being used in your realm of work, and identify at least one tool that is not being used and how
it may be used to benefit your job.
(Note: The answer has to be typed, not hand written nor a picture.) Thank you.
In: Math
A research group conducted an extensive survey of 3144 wage and salaried workers on issues ranging from relationships with their bosses to household chores. The data were gathered through hour-long telephone interviews with a nationally representative sample. In response to the question, "What does success mean to you?" 1508 responded, "Personal satisfaction from doing a good job." Let p be the population proportion of all wage and salaried workers who would respond the same way to the stated question. Find a 90% confidence interval for p. (Round your answers to three decimal places.)
| lower limit | |
| upper limit |
In: Math
The data below are from a study conducted by a consumer research group on the fuel efficiency (rated based on city miles per gallon) of the 30 top-selling U.S. automobiles.
23 20 16 13 34 27
24 10 16 12 34 26
14 31 15 12 16 36
18 22 15 19 28 38
10 16 14 23 19 44
1. Enter the data into a spreadsheet. Be sure to clearly label and neatly format your spreadsheet.
2. Calculate the sum of these data two different ways: a. By writing your own formula. Clearly label the result. b. By using the SUM spreadsheet function. Clearly label the result
. 3. Use the COUNT function to calculate the N of this sample data set. Clearly label the result.
4. Calculate the arithmetic average (mean) of these data by writing your own formula. Clearly label.
5. Create a new column of data in which you subtract the mean fuel efficiency from each individual fuel efficiency score (i.e., MPG – mean). Be sure to use the proper relative and absolute references (indicated with $ signs) to perform these calculations.
6. Now compute the sum, N, and mean of your new (MPG – mean) scores.
7. Create one more new column of data in which you square each of the (MPG – mean) scores. 8. Finally, compute the sum, N, and mean of your new (MPG – mean)^2 scores
In: Math
A group of 1000 students wrote an entrance exam for the University of Statistics. The mean score was 62 with a standard deviation of 12. Assuming a Normal Distribution, answer the following questions:
In: Math
In the last quarter of 2007, a group of 64 mutual funds had a
mean return of 1.9% with a standard deviation of 6.3%. Consider
the Normal model N(0.019,0.063) for the returns of these mutual
funds.
a) What value represents the 40th percentile of these returns?
b) What value represents the 99th percentile?
c) What's the IQR, or interquartile range, of the quarterly
returns for this group of funds?
In: Math
Must show all needed steps in getting to your final answer. And, express your final answer as a decimal.
Show every step NEATLY please
NEATLY AND VERY CLEAR AND READABLE
PLEASE TYPE ANSWER AND WORK
NEATLY AND VERY CLEAR AND READABLE
PLEASE TYPE ANSWER AND WORK
Part 1) Suppose that you are planning to travel a certain air route via plane once each week for your new job. Also, assume that there is a 3% chance that your outbound flight may be cancelled on any given week due to various issues. How many consecutive outbound weekly flights can you fly before the probability of another successful flight (that is, a flight that is not cancelled) drops to 50% or less?
Part 2) Assume that you are playing a game in which you pull a lever and a light comes on. The light will be either red or green. Assume that on any given pull of the lever, P(Red Light) = .40 and P(Green Light) = .60. Find the probability that in pulling the lever 5 times that you will get your 3rd Green Light on the 5th pull of the lever.
Part 3) Suppose in front of you are three boxes that look identical. Further, you are told that one box contains two $1 bills, one contains two $100 bills, and one contains one $1 bill and one $100 bill. You are permitted to choose one box. Then you are asked to remove one bill from the box you chose without looking at the other bill in that box. Suppose that a $100 bill comes out. What is the probability that the other bill in that box is $100?
In: Math
A 2007 Carnegie Mellon University study reported that online
shoppers were willing to pay, on average, more than an extra $0.60
on a $15 purchase in order to have better online privacy
protection.
A sample of ?=22n=22 online shoppers was taken, and each was asked
how much extra would you pay, on a $15 purchase, for better online
privacy protection?'' The data is given below, in $'s.
0.79,0.41,0.67,0.67,0.83,0.76,0.55,0.92,0.61,0.57,0.54,1.25,0.70,0.85,0.59,0.59,0.90,0.67,0.62,0.67,0.44,0.500.79,0.41,0.67,0.67,0.83,0.76,0.55,0.92,0.61,0.57,0.54,1.25,0.70,0.85,0.59,0.59,0.90,0.67,0.62,0.67,0.44,0.50
(a) Do the data follow an approximately Normal distribution? Use
alpha = 0.05. ? yes no
(b) Determine the ?P-value for this Normality test, to three
decimal places.
?=P=
equation editor
Equation Editor
(c) Choose the correct statistical hypotheses.
A.
?0:?>0.60??:?=0.60H0:μ>0.60HA:μ=0.60
B.
?0:?⎯⎯⎯⎯⎯=0.60,??:?⎯⎯⎯⎯⎯<0.60H0:X¯=0.60,HA:X¯<0.60
C.
?0:?>0.60,??:?<0.60H0:μ>0.60,HA:μ<0.60
D.
?0:?⎯⎯⎯⎯⎯=0.60,??:?⎯⎯⎯⎯⎯>0.60H0:X¯=0.60,HA:X¯>0.60
E. ?0:?=0.60,??:?≠0.60H0:μ=0.60,HA:μ≠0.60
F.
?0:?=0.60??:?>0.60H0:μ=0.60HA:μ>0.60
(d) Determine the value of the test statistic for this test, using
two decimals in your answer.
Test Statistic =
equation editor
Equation Editor
(e) Determine the ?P-value for this test, enter your answer to
three decimals.
?=P=
equation editor
Equation Editor
(f) Based on the above calculations, we should ? reject
not reject the null hypothesis. Use alpha = 0.05
In: Math
Describe 2 (two) methods that will be useful in enhancing data quality?
Would internal validity and reliability be correct for this question or would you recommend something else?
In: Math
ANSWER USING R CODE
Using the dataset 'LakeHuron' which is a built in R dataset describing the level in feet of Lake Huron from 1872- 1972. To assign the values into an ordinary vector,x, we can do the following 'x <- as.vector(LakeHuron)'. From there, we can access the data easily. Assume the values in X are a random sample from a normal population with distribution X. Also assume the X has an unknown mean and unknown standard deviation. With this information in mind, answer the following.
a) The sample mean of x
b) the sample mean of 8X
c) Using this data, create a 97% confidence interval for X using the a t-distribution critical value tstar.
d) Using this data, create a 3 percent level test of H0:mu = 578.9 versus the alternative Ha:mu > 578.9. USing tis information, calculate the value of the z-statistic
e) With the z-statistic, calculate the appropriate p-value.
In: Math