Math Homework
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math_probabilities_homework.docxAssignment 3: Problems
Exercises
In the exercises sections in the chapters, of your textbook, Statistics for Management and Economics, perform the following activities:
"Random Variables and Discrete Probability Distributions": 7.84 and 7.97 "Continuous Probability Distributions": 8.35 and 8.42 "Inference about Comparing two Populations": 13.5 and 13.8 "Chi-Squared Tests": 15.48 and 15.56
Submit your answers in a 4- to 5-page Microsoft Word document and import any associated work in Microsoft Excel.
Submit your document to this W3: Assignment 3 Dropbox by Thursday, February 12, 2015.
Cite any sources using the APA format on a separate page.
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Assignment 3 Grading Criteria |
Maximum Points |
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Completed the exercises and imported the required data in Microsoft Excel for "Random Variables and Discrete Probability Distributions". |
10 |
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Completed the exercises and imported the required data in Microsoft Excel for "Continuous Probability Distributions". |
10 |
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Completed the exercises and imported the required data in Microsoft Excel for "Inference about Comparing two Populations". |
15 |
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Completed the exercises and imported the required data in Microsoft Excel for "Chi-Squared Tests". |
15 |
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Total: |
50 |
1. Random Variables and Discrete Probability Distributions": 7.84 and 7.97
· 7.84 Given a binomial random variable with n = 10 and p = .3, use the formula to find the following probabilities.
· a. P(X = 3)
· b. P(X = 5)
· c. P(X = 8)
7.97 In the United States, voters who are neither Democrat nor Republican are called Independents. It is believed that 10% of all voters are Independents. A survey asked 25 people to identify themselves as Democrat, Republican, or Independent.
· a. What is the probability that none of the people are Independent?
· b. What is the probability that fewer than five people are Independent?
· c. What is the probability that more than two people are Independent?
"Continuous Probability Distributions": 8.35 and 8.42
8.35 Xis normally distributed with mean 250 and standard deviation 40. What value of X does only the top 15% exceed?
· 8.42 Travelbyus is an Internet-based travel agency wherein customers can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.
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· a. What is the probability of getting more than 12,000 hits?
· b. What is the probability of getting fewer than 9,000 hits?
Inference about Comparing two Populations": 13.5 and 13.8
· 13.5 In random samples of 25 from each of two normal populations, we found the following statistics:
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x̄1 = 524 |
s1 = 129 |
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x̄2 = 469 |
s2 = 141 |
· a. Estimate the difference between the two population means with 95% confidence.
· b. Repeat part (a) increasing the standard deviations to s1 = 255 and s2 = 260.
· c. Describe what happens when the sample standard deviations get larger.
· d. Repeat part (a) with samples of size 100.
· e. Discuss the effects of increasing the sample size.
13.8 Random sampling from two normal populations produced the following results:
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x̄1 = 412 |
s1 = 128 |
n1 = 150 |
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x̄2 = 405 |
s2 = 54 |
n2 = 150 |
· a. Can we infer at the 5% significance level that μ1 is greater than μ2?
· b. Repeat part (a) decreasing the standard deviations to s1 = 31 and s2 = 16.
· c. Describe what happens when the sample standard deviations get smaller.
· d. Repeat part (a) with samples of size 20.
· e. Discuss the effects of decreasing the sample size.
· f. Repeat part (a) changing the mean of sample 1 to x̄1 = 409
· g. Discuss the effect of decreasing x̄1.
"Chi-Squared Tests": 15.48 and 15.56
15.48 GSS2012* Do foreign-born Americans differ from Americans born in the United States (BORN: 1 = Born in the U.S., 2 = Born elsewhere) in their support of political groups (PARTYID3: 1 = Democrat, 2 = Independent, 3 = Republican)?
American National Election Survey Exercises
Excel users should note that any row containing one or two empty cells must be removed. Use a 5% significance level.
For each of the following variables, conduct a test to determine whether there are differences between the three political party affiliations (PARTY3: 1 = Democrat, 2 = Republican, 3 = Independent).
· 15.55 ANES2008* Know where to vote (KNOW)
· 15.56 ANES2008* Read about campaign in newspaper (READ)
· 15.57 ANES2008* Have health insurance (HEALTH)
· 15.58 ANES2008* Have access to the Internet (ACCESS)
