Evaluate the differences between dependent and independent samples. Provide an example of each type of sample.
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I am curious as to how the "descriptive and inferential statistics physically mean and how they are used in a simulated "real-world" problem" portion should be answered. I spent a long time trying to come up with a way to solve this. Don't be shy. All ideas are welcome.
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Discuss the challenges a researcher would encounter in transforming an area probability face-to-face survey into an Online survey when attempting to estimate the same statistics.
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How does the likelihood function change for Random Vectors vs Random Variables?
Say: If you have Random Variables A1...An with a normal distribution, with mean mu_A and Variance and another Random Variable, B1...Bn, with mean mu_B and Variance...
If there's a random vector C, which equals (a1, ... an, b1, ... bn), and you wanted the likelihood function, would you have two likelihood functions likelihood(a) & likelihood (b) or just one likelihood(a, b)?
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Question 1 The coffee shop A coffee shop knows from past records that its weekly takings (sales) are normally distributed with a mean of $10,500 and a standard deviation of $478. Answer the following questions:
a. Find the probability that in a given week the coffee shop would have takings of more than $10,700
b. Find the probability that in a given week the takings are between $9,800 and $11,000.
c. Calculate the inter-quartile range of weekly takings.
d. What are the maximum weekly takings for the worst 5% of weeks?
Question 2 Normal model
a. A cut-off score of 79 has been established for a sample of scores in which the mean is 67. If the corresponding z-score is 1.4 and the scores are normally distributed, what is the standard deviation?
b. The standard deviation of a normal distribution is 12 and 95% of the values are greater than 6. What is the value of the mean?
c. The mean of a normal distribution is 130, and only 3% of the values are greater than 155. What is the standard deviation?
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You conduct a study to determine the impact that varying the amount of noise in an office has on worker productivity (0 – 25). You obtain the following productivity scores:
|
Low Noise |
Medium Noise |
Loud Noise |
|
15 19 13 13 |
13 11 14 10 |
12 9 7 8 |
For each condition, determine the sample mean and the sample (unbiased) standard deviation. Report the means and standard deviations in a bar graph (include the whiskers on the bars). Write an interpretation of these data including the means and standard deviation.
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3. Testing for equal proportions
Imagine that you are contracted by a local news provider to study consumer demographics in relation to three different types of news media: print (newspaper), Internet, and television. In prior market research, the company has classified each of its customers as receiving news content primarily from only one of these three sources, and as either urban or rural residents. In order to help design effective marketing strategies, you are asked to perform a test for equality of proportions to determine whether there is a significant difference in the proportion of consumers who live in urban versus rural areas for the three media types that are offered.
The three population proportions that you are interested in are:
| p₁ = proportion of urban consumers for the population of newspaper readers | |
| p₂ = proportion of urban consumers for the population of Internet news readers | |
| p₃ = proportion of urban consumers for the population of TV news consumers |
You conduct a hypothesis test with a 0.05 level of significance to determine whether the proportion of urban consumers is the same for all three news sources. The null and alternate hypotheses for your test are:
| H₀: | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Ha:
You collect a random sample of 1,119 consumers of the company’s news content. You find that 212 of the 299 newspaper consumers, 315 of the 379 Internet consumers, and 245 of the 441 TV consumers lived in urban areas. The data are summarized in the following table: Sample Results
Complete the following table of expected frequencies for each population, assuming H₀ is true (round the frequencies to the nearest whole number). (Note: Due to rounding, the row and column totals for your version of this problem may not match the values shown in the table.) Expected Frequencies
To conduct your hypothesis test, you use a chi-square distribution with____ degrees of freedom. The chi-square test statistic for your test is χ² = . Use the following table of selected values of the chi-square distribution to reach a conclusion about your null hypothesis:
With a 0.05 level of significance, you the null hypothesis. You that there is a difference in consumer demographics among the three news media sources. |
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New legislation passed in 2017 by the U.S. Congress changed tax laws that affect how many people file their taxes in 2018 and beyond. These tax law changes will likely lead many people to seek tax advice from their accountants (The New York Times). Backen and Hayes LLC is an accounting firm in New York state. The accounting firms believe that it may have to hire additional accountants to assist with the increased demand in tax advice for the upcoming tax season. Backen and Hayes LLC has developed the following probability distribution for x= number of new clients seeking tax advice.
| x | f(x) |
| 20 | .05 |
| 25 | .20 |
| 30 | .25 |
| 35 | .15 |
| 40 | .15 |
| 45 | .10 |
| 50 | .10 |
a. Is this a valid probability distribution? Explain.
b. What is the probability that Backens and Hayes LLC will obtain 40 or more new clients?
c. What is the probability that Backens and Hayes LLC will obtain fewer than 35 new clients?
d. Compute the expected value, variance, and standard deviation of x.
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Using Baynesian estimation. 1. Let X is Poi(Ꝋ). Let Ꝋ be Γ(α, β). Show that the marginal pmf of X (the compound distribution) is k1(x) = (Γ (α + x) β^x) / (Γ(α) x! (1 + β)^(α+x ); x = 0, 1, 2, 3, …, which is a generalization of the negative binomial distribution.
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A magazine is considering the launch of an online edition. The magazine plans to go ahead only if it is convinced that more than 20% of current readers would subscribe. The magazine contacted a simple random sample of 400 current subscribers, and 102 of those surveyed expressed interest. What should the company do? Test appropriate hypotheses and state your conclusion.
Are the assumptions and the conditions to perform a one-proportion z-test met?
Yes or No
State the null and alternative hypotheses. Choose the correct answer below.
A. H0: p equals=0.20.2
HA: p not equals≠0.20.2
B. H0:p equals=0.20.2
HA:p less than<0.20.2
C. H0:p equals=0.20.2
HA: p greater than>0.20.2
D.The assumptions and conditions are not met, so the test cannot proceed.
Determine the z-test statistic. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. z equals=nothing
(Round to two decimal places as needed.)
B. The assumptions and conditions are not met, so the test cannot proceed.
Find the P-value. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. P-value equals=nothing
(Round to four decimal places as needed.)
B. The assumptions and conditions are not met, so the test cannot proceed.
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This week, we consider how to conduct hypotheses test on one sample data. Discuss the concepts associated with these tests. Consider the following:
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This is a tricky problem. If you want a challenge give this a go. If on the other hand the thought of being a little confused scares you then feel free to sit this problem out (it doesn't count towards participation points). It's a lot harder than anything that will be on your exams and you will not be tested on it. I just want to show you how probability comes up outside of the classroom and I'll explain what the lesson was at the end.
This is a classic question loosely based on an old American Game Show. I'll provide the reference once we've finished the discussion and please don't "google" the answer as that will spoil it! As with all these discussions getting the correct answer isn't the point... it's to encourage you to think about the concepts and discuss.
"You are on a game show and you are shown 3 doors. Behind one door is a car and behind the other 2 are goats but you do not know which is which. You are asked to pick a door. Next the game show host, who know's what's behind the doors, opens one of the two doors that you did not choose revealing a goat. He then asks "Do you want to pick the remaining door or stick with your choice?" Is it to your advantage to switch?
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Given the data set below, use it to answer the following questions:
10, 20, 30, 40, 50
a. Find the standard deviation
b. Add 5 to each data set value and find the standard deviation.
c. Subtract 5 from each value and find the standard deviation.
d. Multiply by 5 on each value and find the standard deviation.
e. Divide by 5 on each value and find the standard deviation.
f. Generalize the results in parts a-e.
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Periodically, customers of a financial services company are asked to evaluate the company's financial consultants and services. Higher ratings on the client satisfaction survey indicate better service, with 7 the maximum service rating. Independent samples of service ratings for two financial consultants are summarized here. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. Use
α = 0.05
and test to see whether the consultant with more experience has the higher population mean service rating.
| Consultant A | Consultant B |
|---|---|
|
n1 = 16 |
n2 = 10 |
|
x1 = 6.85 |
x2 = 6.25 |
|
s1 = 0.68 |
s2 = 0.75 |
State the null and alternative hypotheses.
H0:
μ1 − μ2 = 0
Ha:
μ1 − μ2 ≠ 0
H0:
μ1 − μ2 > 0
Ha:
μ1 − μ2 ≤ 0
H0:
μ1 − μ2 ≠ 0
Ha:
μ1 − μ2 = 0
H0:
μ1 − μ2 ≤ 0
Ha:
μ1 − μ2 = 0
H0:
μ1 − μ2 ≤ 0
Ha:
μ1 − μ2 > 0
(b)
Compute the value of the test statistic. (Round your answer to three decimal places.)
(c)
What is the p-value? (Round your answer to four decimal places.)
p-value =
What is your conclusion?
Reject H0. There is insufficient evidence to conclude that the consultant with more experience has a higher population mean rating.
Reject H0. There is sufficient evidence to conclude that the consultant with more experience has a higher population mean rating.
Do not Reject H0. There is sufficient evidence to conclude that the consultant with more experience has a higher population mean rating.
Do not reject H0. There is insufficient evidence to conclude that the consultant with more experience has a higher population mean rating.
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In a hearing test, subjects estimate the loudness (in decibels)
of sound, and the results are; 12, 68, 74, 66, 37, 52, 71, 90, 65,
76, 73, 22. What are the outer fences?
In a hearing test, subjects estimate the loudness (in decibels) of sound, and the results are; 12, 68, 74, 66, 37, 52, 71, 90, 65, 76, 73, 22. What are the outer fences?
In: Math