Of the travelers arriving at a small airport, 50% fly on major airlines, 20% fly on privately owned planes, and the remainder fly on commercially owned planes not belonging to a major airline. Of those traveling on major airlines, 40% are traveling for business reasons, whereas 60% of those arriving on private planes and 90% of those arriving on other commercially owned planes are traveling for business reasons. Suppose that we randomly select one person arriving at this airport.

(a) What is the probability that the person is traveling on business?

(b) What is the probability that the person is traveling for business on a privately owned plane?

(c) What is the probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons? (Round your answers to four decimal places.)

(d) What is the probability that the person is traveling on business, given that the person is flying on a commercially owned plane?

In an attitude test, 55 out of 120 persons of Community 1 and 115 persons out of 400 of Community 2 answered “Yes” to a certain question. Do these two communities differ fundamentally in their attitudes on this question?

There are twenty stores for a grocery chain in the Mid-Atlantic region. The regional executive wants to visit five of the twenty stores. She asks her assistant to choose five stores and arrange the visit schedule. (Show all work. Just the answer, without supporting work, will receive no credit). (a) Does the order matter in the scheduling? (b) Based on your answer to part (a), should you use permutation or combination to find the different schedules that the assistant may arrange? (c) How many different schedules can the assistant recommend?

Here is a bivariate data set.

x	y
50.4	96.8
53.7	27.6
-17.6	158.6
49.9	-48.1
30.5	-6.1
36.7	179
43.5	-3.9
40.5	65.1
52.1	-129.7
43.5	85.1
33.4	-41.4
63.4	-50
25.3	31.8
41.2	11.8
34.4	149.4
50.5	-50.5

Find the correlation coefficient and report it accurate to three decimal places.
r =

The accompanying data file shows the square footage and associated property taxes for 20 homes in an affluent suburb 30 miles outside of New York City. Estimate a home’s property taxes as a linear function of its square footage. At the 5% significance level, is square footage significant in explaining property taxes? Show the relevant steps of the test.

Please use Minitab and explain the various steps involved.

Property Taxes	Square Footage
21928	2449
17339	2479
18229	1890
15693	1000
43988	5665
33684	2573
15187	2200
16706	1964
18225	2092
16073	1380
15187	1330
36006	3016
31043	2876
42007	3334
14398	1566
38968	4000
25362	4011
22907	2400
16200	3565
29235	2864

1. Young children in the U.S. are exposed to an average of 4 hours of television per day, which can adversely impact a child’s well-being. You are working in a research lab that hypothesizes that children in low income households are exposed to more than 4 hours of television. In order to test this hypothesis, you collected data on a random sample of 75 children from low income households. You found a sample mean television exposure time of 4.5 hours. Based on a previous study, you are willing to assume a population standard deviation of 0.5 hours. a. Using this information, test your hypothesis using the critical value approach; assume a significance level of 10%. b. Calculate the p-value associated with your test statistic. Using the p-value approach, what is your hypothesis test conclusion?

The population average cholesterol content of a certain brand of egg is 215 milligrams, and the standard deviation is 15 milligrams. Assume the variable is normally distributed.

(a) Find the probability the cholesterol content for a single egg is between 210 and 220.

(b) Find the probability the average cholesterol contentfor 25 eggs is between 210 and 220.

(c) Find the third quartile for the average cholesterol content for 25 eggs.

(d) If we are told the average for 25 eggs is less than 220mg, what is the probability the average is less than210 mg?

State the likely relative positions of the mean, median, and mode for the following distributions:

Family income in large city

Scores on a very easy exam

Heights of a large group of 25-year old males

The number of classes skipped during the year for a large group of undergraduate

Terri Vogel, an amateur motorcycle racer, averages 129.71 seconds per 2.5 mile lap (in a seven-lap race) with a standard deviation of 2.28 seconds. The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps.

• Part (a)

  In words, define the random variable X.

  the time (in seconds) per lapthe time (in seconds) per race    the distance (in miles) of each racethe distance (in miles) of each lap

• Part (b)

  Give the distribution of X.
  X ~

• Part (c)

  Find the percent of her laps that are completed in less than 135 seconds. (Round your answer to two decimal places.)
  

• Part (d)

  The fastest 2% of her laps are under how many seconds? (Round your answer to two decimal places.)
  sec

• Part (e)

  Enter your answers to two decimal places.
  
  The middle 80% of her lap times are from  seconds to  seconds.

In a randomized controlled​ trial, insecticide-treated bednets were tested as a way to reduce malaria. Among 322 infants using​ bednets, 13 developed malaria. Among

276 infants not using​ bednets, 29 developed malaria. Use a 0.05 significance level to test the claim that the incidence of malaria is lower for infants using bednets. Do the bednets appear to be​ effective? Conduct the hypothesis test by using the results from the given display.

please show me how to do on ti-84

Difference=​p(1)minus−​p(2)

Estimate for​ difference: - 0.0646998

95% upper bound for​ difference: - 0.02261687

Test for difference=0 ​(vs <​ 0): Z=- 3.09  

​P-Value=0.001

A study was done on body temperatures of men and women. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Complete parts​ (a) and​ (b) below. Use a 0.01 significance level for both parts.

Men                 Women

μ          μ1                    μ2

n          11                    59

x          97.78°F           97.25°F

s           0.97°F             0.66°F

a. Test the claim that men have a higher mean body temperature than women.

What are the null and alternative​ hypotheses?

A. H0​: μ1≥μ2

H1​: μ1<μ2

B. H0​: μ1=μ2

H1​: μ1≠μ2

C. H0​: μ1=μ2

H1​: μ1>μ2

D. H0​: μ1≠μ2

H1​: μ1<μ2

The test​ statistic, t, is _____. ​(Round to two decimal places as​ needed.)

The​ P-value is _____. ​(Round to three decimal places as​ needed.)

State the conclusion for the test.

A. Reject the null hypothesis. There is not sufficient evidence to support the claim that men have a higher mean body temperature than women.

B. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that men have a higher mean body temperature than women.

C. Reject the null hypothesis. There is sufficient evidence to support the claim that men have a higher mean body temperature than women.

D. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that men have a higher mean body temperature than women.

b. Construct a confidence interval suitable for testing the claim that men have a higher mean body temperature than women.

_____<μ1−μ2<_____ ​(Round to three decimal places as​ needed.)

You download two sets of posts from an online forum. Set One is a collection of posts by "pro-Hong Kong Protestors" (HKP) students. Set Two is a collection of posts by pro-Chinese Government (CG) students. (Let's say you get these two collections by searching for students who are members either of a pro-HKP group, or pro-CG group.) You compute the probabilities of different words they use, and focus on a set of six "key" words of interest, {"legal", "democracy", "violence", "legitimate", "calm", "foreign"}. You compute the "probability that, given that they use one of these five words, which word it is" (you could do this by counting up each of those words for the two sets, and dividing by the total number of those words in each set.) words: {"legal", "democracy", "violence", "legitimate", "calm", "foreign"}. pHKP = {0.2, 0.2, 0.3, 0.2, 0.05, 0.05} pCG = {0.1, 0.05, 0.3, 0.05, 0.1, 0.4}

The government tells you that they think about 10% of the posters on the mainland are pro-HKP, and they just want to have a conversation with these people about things.

You encounter a post. The poster uses the word "democracy" twice, the word "violence" once, and the word "foreign" once. Assuming that he is either pro-HKP, and follows the pHKP distribution, or pro-CG, and follows the pCG distribution...

Q: Given government priors, what is the probability that the poster is pro-HKP? (i.e., follows the pHKP distribution rather than the pCG distribution)

Use the Multiplication Rule to find the number of positive divisors of 20!. Include a procedure that “builds” such divisors

Suppose that a company's sales increase when the economy is doing well. Also, suppose that the
company's advertising budget is based upon the number of sales, and that larger sales lead to a larger
advertising budget.
A There is an association between how well the economy is doing and the company's advertising budget.
B There is a causal relationship between the company's sales and the company's advertising budget.
C Both of the above.
D Neither of the above.

Project Assignment The purpose of this assignment is for you to gain practice in applying the concepts and techniques we learned in class. In order to complete the assignment, please do the following:

1. find or create a data set containing values of at least one interval or ratio variable for at least one-hundred cases (n >= 100); 1

2. provide basic descriptive statistics to summarize the central tendency and variability of the data;

3. provide at least one table (see chapter 2: frequency, percentage, cumulative frequency, or cumulative percentage) summarizing the distribution of the data;

4. provide a graph (see chapter 3: histogram, line graph, or time series graph) that illustrates a salient or important property or set of properties of the data;

5. calculate a confidence interval for the value of the variable; and

6. conduct a hypothesis test using the data.

Write a short paper (~2-4 pages double spaced) summarizing your work. Be sure to clearly describe your findings, why you chose to analyze the data as you did, and what your results mean. For example, if you chose to summarize the data’s variability using the interquartile range (as opposed to the standard deviation), explain why you made this choice. Be sure to be as specific and clear as possible about the rationale underlying your choices and about your findings.

1 Note that projects analyzing a nominal or ordinal variable will receive no credit (i.e., a grade of zero).