A basketball team has 5 players, 3 in ‘‘forward” positions (this includes the ‘‘center”) and 2 in ‘‘guard” positions.

How many ways are there to pick a team if there are 6 forwards, 4 guards, and 2 people who can play forward or guard?

The American Community Survey is a survey that uses U.S. census data to compile information on various characteristics of the U.S. population. Here are statistics that I would like you to analyze from a sample of states. The independent variable (x-variable) is the percent of the state population living below the poverty level. The dependent variable (y-variable) is the state infant mortality rate in deaths per 1000 births. The data is displayed in the following table: State: Percent of Population living below poverty level Infant Mortality Rate Deaths per 1000 Births Vermont 11.5 5.12 New Jersey 10.2 5.35 Georgia 19.1 8.02 Kentucky 19.1 7.04 Iowa 12.8 5.43 Kansas 13.8 7.50 Colorado 13.5 6.04 New Mexico 21.5 5.81 Arizona 19.0 6.54 California 16.6 5.12 Oregon 17.5 5.41 North Dakota 12.2 6.44 Ohio 16.4 7.74 Maine 14.1 6.04 Mississippi 22.6 10.16 Arkansas 19.5 7.89 Louisiana 20.4 9.38 Wisconsin 13.1 6.57 Connecticut 10.9 6.27 Wyoming 11.3 7.05

How much of the variation in state mortality rates can be explained by the linear model which uses “poverty rate” data as a predictor? a. 33% b. 57.4% c. 55.8% d. 78% e. 62%

1. An experiment consists of drawing two marbles from a box containing red, yellow, and green marbles. One event in the sample space is RR. What are all of the events in the sample space? (Note: order matters) (3)

2. In a certain large population, 46% of households have a total annual income of over $70,000. A simple random sample is taken of four of these households. What is the probability that more than 2 of the households in the survey have an annual income of over $70,000?                                                                (8)

3. Which would you expect to have a higher standard deviation: data scores that are spread out or data scores that are close together?   
4. In a survey of U.S. households, 588 had home computers while 722 did not. Use this sample to estimate the probability of a household having a home computer.

1. Home Security Systems is studying the time utilization of its sales force. A random sample of 40 sales calls showed that the representatives spend an average of ẍ = 44 minutes on the road with a standard deviation of s = 6 minutes for each sales call.

1. Create a line showing the mean and values for 4 standard deviations above and 4 standard deviations below the mean.                                                                                                                                                (2)

2. Use Chebyshev’s Theorem to find the values between which we can expect at least 89% of the data to fall.                                                                                                                                                                       (2)

3. At least what percent of the data can we expect to fall between 38 and 50 minutes using the Empirical Rule?                                                                                                                                                        (2)

A psychologist studied the number of puzzles subjects were able to solve in a five-minute period while listening to soothing music. Let X be the number of puzzles completed successfully by a subject. The psychologist found that X had a distribution where the possible values of X are 1, 2, 3, 4 with the corresponding probabilities of 0.2, 0.4, 0.3, and 0.1. Use this information to answer questions 20-23 below.

2. Does the above data form a probability distribution? Create the distribution and explain why or why not.(5)

3. Using the above data, what is the probability that a randomly chosen subject completes at least three puzzles in the five-minute period while listening to soothing music?                                                                   (2)

4. Using the above data, the mean µ of X is what? Show work.                                                                             (3)
5. Using the above data (on previous page), the standard deviation σ of X is what? Show work.                      (4)

1. Why would we use the 10-90 percentile range?                                                                                                  +2

2. A data set has a range of 348. Use the range rule of thumb to determine the standard deviation.        +1

A batch of 26 light bulbs includes 5 that are defective. Two light bulbs are randomly selected. If the random variable, X, represents the number of defective light bulbs which can be selected, what values can X have?                

1. I need to fuel my car every week. Based on my observation, the price of gas really follows a Markov Chain. The price can be 3.2 dollars, 3.3 dollars or 3.4 dollars for one gallon. If the price for this week is 3.2 dollars, the price of next week will be 3.2, 3.3 and 3.4 with the probability of 0.4, 0.4 and 0.2 respectively. If the price for this week is 3.3 dollars, the price of next week will be 3.2, 3.3 and 3.4 with the probability for 0.2, 0.5 and 0.3 respectively. If the price for this week is 3.4 dollars, the price of next week will be 3.2, 3.3 and 3.4 with probability 0.3, 0.3 and 0.4 respectively.
   1. Please give out the transition matrix.
   2. For one year, how much should I pay for the gas for my car? (Assume 52 weeks/year and I use 10 gallons every week).
   3. If the price of this week is 3.2 dollars, what is the probability that I will observe 3.3 dollars price after 2 weeks?

If the price of this week is 3.2 dollars, I will observe 3.3 dollars price for the first time after how many weeks in average?

A university would like to estimate the proportion of fans who purchase concessions at the first basketball game of the season. The basketball facility has a capacity of 3 comma 600 and is routinely sold out. It was discovered that a total of 200 fans out of a random sample of 500 purchased concessions during the game. Construct a​ 95% confidence interval to estimate the proportion of fans who purchased concessions during the game. The​ 95% confidence interval to estimate the proportion of fans who purchased concessions during the game is left parenthesis nothing comma nothing right parenthesis . ​(Round to three decimal places as​ needed.)

A factory has a buffer with a capacity of 4 m³ for temporarily storing waste produced by the factory. Each week the factory produces k m³ waste with a probability p_k, where p₀=1/8, p₁=1/2, p₂=1/4 and p₃=1/8. If the amount of waste produced in one week exceeds the remaining capacity of the buffer, the excess is specially removed at a cost of 30 per m³. At the end of each week there is a regular opportunity to remove the waste from the storage at a fixed cost of 25 and a variable cost of 5 per m³. The following policy is used. If at the end of the week the storage buffer contains more than 2 m³, the buffer is emptied; otherwise, no waste is removed. Determine the ling-run average cost per week. You need to define the states and the transition probability matrix well first.

How can u solve the following question by using the method: Computing trend and seasonal factor from linear regression line (without excel)

Question:

The following table shows the past two years of quarterly sales information. Assume that there are both trend and seasonal factors and that the seasonal cycle is one year.

sales per quarter: 215, 240, 205, 190, 160, 195, 150, 140

23. Suppose that a large Introduction to Psychology class has taken a midterm exam, and the scores are normally distributed with a mean of 75 and a standard deviation of 9. a. What proportion of the class got scores above 90? b. What percent of the class got scores below 78? c. What percent of the class got scores above 68? d. What proportion of the class got scores below 94

Problem: For each region described, use the normal table to find the proportion of observations from a standard normal distribution that are in the region. Show any calculations and sketch a relevant picture for each. Z < −.57

Determine the independent and dependent variable in each of the following scenarios:

a. The relationship between smoking and lip cancer

b. The relationship between income and the highest level of education attained -

It is known that 20% of products on a production line are defective. a. Randomly pick 5 products. What is the probability that exactly 2 are defective? b. Products are inspected until first defective is encountered. Let X = number of inspections to obtain first defective. What is the probability that X=5?

Isle Royale, an island in Lake Superior, has provided an important study site of wolves and their prey. Of special interest is the study of the number of moose killed by wolves. In the period from 1958 to 1974, there were 296 moose deaths identified as wolf kills. The age distribution of the kills is as follows.

Age of Moose in Years	Number Killed by Wolves
Calf (0.5 yr) 1-5 6-10 11-15 16-20	108 47 75 60 6

(a) For each age group, compute the probability that a moose in that age group is killed by a wolf. (Round your answers to three decimal places.)

0.5
1-5
6-10
11-15
16-20

(b) Consider all ages in a class equal to the class midpoint. Find the expected age of a moose killed by a wolf and the standard deviation of the ages. (Round your answers to two decimal places.)

μ	=
σ	=

The Toylot company makes an electric train with a motor that it claims will draw an average of only 0.8 ampere (A) under a normal load. A sample of nine motors was tested, and it was found that the mean current was x = 1.34 A, with a sample standard deviation of s = 0.49 A. Do the data indicate that the Toylot claim of 0.8 A is too low? (Use a 1% level of significance.)

What are we testing in this problem?

Answer: single proportions.

(a) What is the level of significance?
Answer: 0.01

State the null and alternate hypotheses.

H₀: μ ≠ 0.8; H₁: μ = 0.8

H₀: p = 0.8; H₁: p > 0.8    

H₀: μ = 0.8; H₁: μ ≠ 0.8

H₀: p = 0.8; H₁: p ≠ 0.8

H₀: p ≠ 0.8; H₁: p = 0.8

H₀: μ = 0.8; H₁: μ > 0.8

(b) What sampling distribution will you use? What assumptions are you making?

The standard normal, since we assume that x has a normal distribution with known σ.

The Student's t, since we assume that x has a normal distribution with unknown σ.    

The standard normal, since we assume that x has a normal distribution with unknown σ.

The Student's t, since we assume that x has a normal distribution with known σ.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Find (or estimate) the P-value.

P-value > 0.250

0.125 < P-value < 0.250

0.050 < P-value < 0.125

0.025 < P-value < 0.050

0.005 < P-value < 0.025

P-value < 0.005

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.   

At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

Answer: There is sufficient evidence at the 0.01 level to conclude that the toy company claim of 0.8 A is too low.

(07.01 MC) Poisoning by the pesticide DDT causes tremors and convulsions. In a study of DDT poisoning, researchers fed several rats a measured amount of DDT. They then measured electrical characteristics of the rats' nervous system that might explain how DDT poisoning causes tremors. One important variable was the "absolute refractory period"—the time required for a nerve to recover after a stimulus. This period varies Normally. Measurements of the absolute refractory period, in milliseconds, for four rats were 1.7, 1.8, 1.9, and 2.0.

Part A: Find the mean refractory period x and the standard error of the mean. (2 points)

Part B: Calculate a 90% confidence interval for the mean absolute refractory period for all rats of this strain when subjected to the same treatment. (4 points)

Part C: Suppose the mean absolute refractory period for unpoisoned rats is known to be 1.3 milliseconds. DDT poisoning should slow nerve recovery and thus increase this period. Do the data give good evidence for this supposition? What can you conclude from a hypothesis test? Justify your response with statistical reasoning. (4 points) (10 points)

A die is tossed 600 times. H0 is the hypothesis that the proportion of tosses showing aces is binomially distributed with mean 1/6. Find the upper limit of the region for which H0 is accepted at the 1% level of significance in a two sided test.

A. .240

B. .243

C. .206

D. .252

E. .258