Demand data on "Service Orders" for a particular service enterprise for the previous 12 months is as follows: 550, 652, 673, 707, 725, 752, 780, 797, 815, 836, 850, and 872. Problem 3b) Use the following three methods and prepare three forecasting tables with errors for the given demand data. • a 3-month Weighted Moving Average with the weights 0.6, 0.3, and 0.1 with the maximum weight going for the most recent data point into the past • Exponential Smoothing with smoothing constant = 0.9 • Linear Trend Regression
In: Math
Suppose a geyser has a mean time between eruptions of 66 minutes. If the interval of time between the eruptions is normally distributed with standard deviation
24 minutes, answer the following question.
What is the probability that a random sample of 38 time intervals between eruptions has a mean longer than 76 minutes?
The probability that the mean of a random sample of 38 time intervals is more than 76 minutes is approximately __________
(Round to four decimal places as needed.)
In: Math
A Gallup Poll released in December 2010 asked 1019 adults living in the Continental U.S. about their belief in the origin of humans. These results, along with results from a more comprehensive poll from 2001 (that we will assume to be exactly accurate), are summarized in the table below:
| Response | Year: 2010 | Year: 2001 |
|---|---|---|
| Humans Evolved with God guiding (1) | 38% | 37% |
| Humans evolved but God had no part in the process (2) | 16% | 12% |
| God created humans in present form (3) | 40% | 45% |
| Other / No opinion (4) | 6% | 6% |
Calculate the actual number of respondents in 2010 that fall in each response category as well as the expected number, assuming that the population follows the 2001 distribution. (please round to the nearest whole number)
| Response | Observed 2010 | Expected 2010 |
|---|---|---|
| Humans Evolved with God guiding (1) | ||
| Humans evolved but God had no part in the process (2) | ||
| God created humans in present form (3) | ||
| Other / No opinion (4) |
Conduct a chi-square test and state your conclusion.
The value of the test statistic is: .... (please round to two decimal places)
The p-value for this test is: .... (please round to four decimal places; you can use CHISQ.DIST Excel function)
State the conclusion.
In: Math
The mayor of a large city claims that 25 % of the families in the city earn more than $ 100,000 per year; 55 % earn between $ 30,000 and $ 100,000 (inclusive); 20 % earn less than $ 30,000 per year.
In order to test the mayor’s claim, 285 families from the city are surveyed and it is found that:
90 of the families earn more than $ 100,000 per year;
135 of the families earn between $ 30,000 and $ 100,000 per year
(inclusive);
60 of the families earn less $ 30,000.
Test the mayor’s claim based on 2.5 % significance level.
In: Math
* Make sure you turn in your code (take a screen shot
of your code in R)and answers. Conduct the hypothesis
and solve questions by using R.
2) A random sample of 12 graduates of a secretarial school averaged
73.2 words per minute
with a standard deviation of 7.9 words per minute on a typing test.
What can we conclude,
at the .05 level, regarding the claim that secretaries at this
school average less than 75
words per minute on the typing test? (You may treat the number of
words that a secretary
types in one minute as being normally distributed.)
In: Math
The number of buses that arrive at a bus stop during a one-hour time span can be modeled as a Poisson process with rate λ (see Remark below). Now suppose a passenger has just arrived at the bus stop and starts waiting. Let Y be the time (in unit of hours) she needs to wait to see the first bus.
(a) Is Y a discrete or continuous random variable? Find the set of all possible values of Y .
(b) For a possible value y of Y , find P(Y > y).
(c) Find the distribution (pdf/pmf) of Y and identify it as one of the “named” distributions with corresponding parameter(s).
In the same setting as in the previous question, suppose we know there is exactly one bus arrival on a time interval [0, 1] (the unit is hour). Let Y be this single arrival time.
(d) Find the set of possible values of Y .
(e) For a possible value y of Y , find P(Y ≤ y).
(f) Find the pdf/pmf of Y and identify it as one of the “named” distributions with corresponding parameter(s).
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A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x overbar, is found to be 110, and the sample standard deviation, s, is found to be 10. (a) Construct an 80% confidence interval about mu if the sample size, n, is 28. (b) Construct an 80% confidence interval about mu if the sample size, n, is 13. (c) Construct a 70% confidence interval about mu if the sample size, n, is 28. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
In: Math
A person wants to invest $10,000 into stocks: a high tech company (T) with an expected annual return of 12% and a risk index of 8; and a regulated power company (P) with an expected annual return of 6% and a risk index of 2. To limit risk, the combined portfolio risk must be no more than 6 and the proportion of investment in T must be less than 60%. Find the portfolio that will maximize the annual return R while meeting the risk limitations.
a. Formulate the Investment Portfolio problem with the requirement of investing up to $10,000, and solve it graphically.
b. Compute the increase in annual return if the total investment is increased by $1,000.
c. Compute the increase in annual return if the constraint of portfolio risk index is increased from 6 to 7.
In: Math
Here is a list of scores on the Traditionalism Index for the ANES unique group of
respondents who simultaneously rated Christian Fundamentalists and Atheists
at 100 on the Feeling Thermometer:
7, 10, 5, 6, 5, 8, 5, 12, 4, 11, 11, 9, 10, 13, 8, 8, 7
Use these raw data to the find the mean, median, mode, variance, and standard
deviation.
In: Math
A trucking company wants to find out if their drivers are still alert after driving long hours. So, they give a test for alertness to two groups of drivers. They give the test to 400 drivers who have just finished driving 4 hours or less and they give the test to 585 drivers who have just finished driving 8 hours or more. The results of the tests are given below.
Passed Failed
Drove 4 hours or less 310 90
Drove 8 hours or more 415 170
Is there is a relationship between hours of driving and alertness? (Do a test for independence.) Test at the 1 % level of significance.
In: Math
Case studies showed that out of 10,409 convicts who escaped from certain prisons, only 7958 were recaptured.
(a) Let p represent the proportion of all escaped
convicts who will eventually be recaptured. Find a point estimate
for p. (Round your answer to four decimal places.)
(b) Find a 99% confidence interval for p. (Round your
answers to three decimal places.)
| lower limit | |
| upper limit |
In: Math
A simple random sample of checks were categorized based on the number of cents on the written check and recorded below. Cents Category 0¢-24¢ 25¢-49¢ 50¢-74¢ 75¢-99¢ Frequency 58 37 28 17 Use the p-value method and a 5% significance level to test the claim that 50% of the check population falls into the 0¢-24¢ category, 20% of the check population falls into the 25¢-49¢ category, 16% of the check population falls into the 50¢-74¢ category, and 14% of the check population falls into the 75¢-99¢ category. Calculate the expected value for the 50¢-74¢ category (round to the nearest tenth).
In: Math
The United States Centers for Disease Control and Prevention (CDC) found that 17.9%17.9% of women ages 1212–5959 test seropositive for HPV‑16. Suppose that Tara, an infectious disease specialist, assays blood serum from a random sample of n=1000n=1000 women in the United States aged 1212–59.59.
Apply the central limit theorem for the distribution of a sample proportion to find the probability that the proportion, ^p,p^, of women in Tara's sample who test positive for HPV‑16 is greater than 0.1990.199. Express the result as a decimal precise to three places.
P(^p>0.199)=
Apply the central limit theorem for the distribution of a sample proportion to find the probability that the proportion of women in Tara's sample who test positive for HPV‑16 is less than 0.1740.174. Express the result as a decimal precise to three places.
P(^p<0.174)=
In: Math
(Please answer this question accuratelly THANKS)
The following commands in R computes 5000 simulations of sample means of size 12 from a normal distribution with mean µ = 100 and standard deviation σ = 14. require
(fastR2) nsamplesum <- do(5000) * c(sample.mean=mean(rnorm(12,100,14)))
The following commands compute the approximate mean and standard deviation of the sample mean and plot the histogram giving the approximate distribution of the sample mean.
mean(∼ sample.mean, data=nsamplesum) sd(∼ sample.mean, data=nsamplesum) gf dhistogram(∼ sample.mean, data= nsamplesum, bins=20)
(a) Compare the approximate values of mean and standard deviation of the sample mean found above with the expected theoretical ones.
(b) Repeat the same simulation as above using now samples from a uniform distribution in the interval [−2, 4]. Also in this case, run a numerical test over 5000 simulations, compute mean and standard deviation of the sample mean, and compare it to the theoretical result.
In: Math
Compare the kk-NN classifier, linear discriminant analysis (LDA) and the logistic model when it comes to classification. Which is generally better?
In: Math