# Project #36398 - Statistics

All work must be done in word format with accompaning excel sheets showing work:

1.  Given a binomial random variable with n = 10 and p = .3, use the formula to find the following probabilities.

1. P(X = 3)

2.  P(X = 5)

3. P(X = 8)

Answer Key:   a. .2668 b. 1029 c. .0014

2.  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.

1. What is the probability that none of the people are Independent?

2.  What is the probability that fewer than five people are Independent?

3.  What is the probability that more than two people are Independent?

3.  Xis normally distributed with mean 250 and standard deviation 40. What value of X does only the top 15% exceed?

4.  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.

a. What is the probability of getting more than 12,000 hits?

b. What is the probability of getting fewer than 9,000 hits?

5.  In random samples of 25 from each of two normal populations, we found the following statistics:xÌ„1 = 524s1 = 129xÌ„2 = 469s2 = 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.

6.  Random sampling from two normal populations produced the following results

xÌ„1 = 412                 s1 = 128            n1 = 150

xÌ„2 = 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 xÌ„1 = 409

g. Discuss the effect of decreasing xÌ„1.

a. t = .62, p-value = .2689; no

b.  t = 2.46, p-value = .0074; yes

c.  The t-statistic increases and the p-value decreases.

d.  t = .23, p-value = .4118

e. The t-statistic decreases and the p-value increases.

f.  t = .35, p-value = .3624

g. The t-statistic decreases and the p-value increases.

7.    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)?

Answer Key:      χ2 = 25.90, p-value = 0; yes

8. 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). Excel users should note that any row containing one or two empty cells must be removed. Use a 5% significance level.

Answer Key:   χ2 = 5.89, p-value = .0525; no

 Subject Mathematics Due By (Pacific Time) 07/26/2014 12:00 am
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