An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities.

If required, round your answers to two decimal places.

In a new promotional activity at Starbucks, whenever you buy a coffee, they give you fortune cookie, on which there is the digit 1,2, or 3, i.e., one of them. So whenever, you buy a coffee, you look at the number and if it is a number that you do not have it, then you collect that number. When you collect the numbers 1,2, and 3, then Starbucks gives you a free coffee.

(a) If X represents the number of coffees you need to purchase in order to get a free coffee, determine PMF of X for X values only until 5. No need to get the PMF for the other values of X since there will be two many cases.

(b) As we can see in Part a, the PMF calculation will be too hectic for the next values of X. Hence, the calculation for the parameters like mean and variance would be difficult. However, we can determine the mean of this distribution by using the concept of geometric distribution. After modeling your problem at hand with geometric distribution, determine how many coffees you need to purchase to get a free coffee?

Question 4

It has been hypothesized that the distribution of seasonal colds in Canada is as follows:

A random sample of 200 Canadian citizens provided the following results:

10 marks     Do the observed data contradict the hypothesis? Formulate and test the appropriate hypotheses at the 5% level of significance. Use the critical value approach.

1. Indicate which type of t-test would be appropriate. You can choose between the one sample t-test, dependent samples t-test and independent samples t-test. Write down the null and alternative hypotheses.

(a) In a sample of 20 newborn Russian Blue kittens, the mean weight was 3 ounces with a standard deviation of 0.5 ounces. In a sample of 20 newborn Turkish Van kittens, the mean weight was 5 ounces with a standard deviation of 0.6 ounces. On average, are the birth weights of Russian Blue kittens different from those into Turkish Van kittens?

(b) 12 normal (“wild type”) and 13 cyclin d2 knockout mice (mutants) were placed in devices which recorded their locomotor activity. The mean and standard deviation of activity for the former group were 112 and 36, while those for the latter were 200 and 25. Do the two mouse genotypes differ in average amount of locomotor activity?

(c) A sample of 25 students from a certain school have a mean SAT score of 1200 points. Suppose the general population of test-takers has a mean of 1060 points and a standard deviation of 110 points. On average, do students from the school in question score higher than the general population?

(d) Mice used in research come in different strains (a bit like breeds of dog or cat). These can differ in characteristics such as the startle response, i.e. how forcefully the animal flinches when it hears a loud sudden noise. Some researchers wanted to find a mouse strain with a strong startle response as a basis for a line of mutants. They therefore compared the startle response in 10 mice of the C57BL/6J strain and 10 mice of the 129X1/SvJ strain.

(e) Amphetamine has been found in some cases to reduce the startle response of mice. Quinpirole is drug that acts on some of the same neurotransmitters as amphetamine but is more selective and has a different mechanism. Researchers wondered therefore whether quinpirole would reduce the startle response in mice. They therefore injected 10 mice with quinpirole and 10 mice with saline (as a control) and measured their startle response to loud noises.

(f) Imagine the same situation as (e) above, except that instead of injecting each mouse only once with either quinpirole or saline, all 20 mice are given both injections on separate days. For example, mouse #1 gets saline and has his startle response tested, then several days later receives quinpirole and his startle response is tested again.

(g) Now imagine the same situation as (e) above except that all 20 mice are tested once, with quinpirole, and their startle response is com- pared to the previously published population mean and standard deviation of startle responses for mice without quinpirole (this is not how you would do the experiment in real life).

For large U.S. companies, what percentage of their total income comes from foreign sales? A random sample of technology companies (IBM, Hewlett-Packard, Intel, and others) gave the following information.†

Another independent random sample of basic consumer product companies (Goodyear, Sarah Lee, H.J. Heinz, Toys 'R' Us) gave the following information.

Assume that the distributions of percentage foreign revenue are mound-shaped and symmetric for these two company types.

(a) Use a calculator with mean and standard deviation keys to calculate x₁, s₁, x₂, and s₂. (Round your answers to two decimal places.)

(b) Let μ₁ be the population mean for x₁ and let μ₂ be the population mean for x₂. Find a 98% confidence interval for μ₁ − μ₂. (Round your answers to two decimal places.)

An experimental surgical procedure is being studied as an alternative to the old method. Both methods are considered safe. Five surgeons preform the operation on two patients matched by age, sex, and other relevant factors, with the results shown. The time to complete the surgery (in minutes) is recorded. At the 5% significance level, is the new way faster?

*Do not use p-values

*Use and show the 5 step method

D-bar=

S_d=

Step 1: H₀=

H_A=

Step 2: alpha =

Step 3: Test Statistic:

Step 4: Decision Rule:

Step 5: Calculation and Decision

Reject or do not reject H₀? Why?

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.

If we are told the average for 25 eggs is less than 220 mg, what is the probability that the average is less than 210?

Round the answers to four decimal places.

Independent random samples of professional football and basketball players gave the following information.

Heights (in ft) of pro football players: x₁; n₁ = 45

Heights (in ft) of pro basketball players: x₂; n₂ = 40

(a) Use a calculator with mean and standard deviation keys to calculate x₁, s₁, x₂, and s₂. (Round your answers to three decimal places.)

(b) Let μ₁ be the population mean for x₁ and let μ₂ be the population mean for x₂. Find a 90% confidence interval for μ₁ – μ₂. (Round your answers to three decimal places.)

Statistics Anxiety

1.) Your Experiences: Share an experience you’ve had with statistics/math anxiety or test anxiety?

2.) Your Approach: What will be your approach to overcome anxiety statistics or math course?

R Simulation:Write an R code that does the following:

(a) Generate n samples x from a random variable X that has a uniform density on [0,3].

(b) Now generate samples of Y using the equation: y = α x + β

(c) For starters, set α = 1, β = 1.

In a recent year, according to the Bureau of Labor Statistics, the median number of years that wage and salary workers had been with their current employer (called employee tenure) was 3.5 years. Information on employee tenure has been gathered since the early 1950's using the Current Population Survey (CPS), a monthly survey of 50,000 households that provides information on employment, unemployment, earnings, demographics, and other characteristics of the U. S. population. With respect to employee tenure, the questions measure how long workers had been with their current employer, not how long they plan to stary with their employer.

Employee Tenure of 20 workers

4.1, 2.3, 3.5, 4.6, 3.1, 1.2, 3.9, 2.1, 1.0, 4.5, 3.2, 3.4, 4.1, 3.1, 2.8, 1.4, 3.4, 4.9, 5.7, 2.6

A) A congressional representative claims that the median tenure for workers from the representative's district is less than the national median tenure of 3.5 years. Thae claim is based on the representative's data shown above. Assume that the employees were randomly selected.

1) How would you test the representative's claim?

2) Can you use a parametric test, or do you need a nonparametric test? Why?

3) State the null and alternative hypothesis.

4) Test the claim using alpha = 0.05. What can you conclude? Show your work, the process that you used, and the result.

Employee tenure for a sample of male workers

3.3, 3.9, 4.1, 3.3, 4.4, 3.3, 3.1, 4.1, 2.7, 4.9, 0.9, 4.6

Employee tenure for a sample of female workers

3.7, 4.2, 2.7, 3.6, 3.3, 1.1, 4.4, 4.4, 2.6, 1.5, 4.5, 2.0

B) A congressional representative claims that the median tenure for male workers is greater that the median tenure for female workers. The claim is based on the data shown above.

5) How would you est the representative's claim?

6) Can you use a parametric test, or do you need to use a nonparametric test?

7) State the null hypothesis and the alternative hypothesis.

8) Test the claim using alpha = 0.05. What can you conclude. Show your work, the process that you used, and the result.

This question is based on a Poisson discrete probability distribution. The distribution is important in biology and medicine, and can be dealt with in the same way as any other discrete distribution. Red blood cell deficiency may be determined by examining a specimen of blood under the microscope. The data in Table B gives a hypothetical distribution of numbers of red blood cells in a certain small fixed volume of blood from normal patients. Theoretically, there is no upper limit to the value of a POISSON distribution. In reality, you can force only so many red blood cells into a given volume.  Copy the data from Table B into columns of the EXCEL worksheet, name the columns, and view the table.]

8. What is the probability that a blood sample from this distribution will have exactly 20 red blood cells?

9. What is the probability that a blood sample from a normal person will have between 19 and 26 red blood cells? HINT: See questions 3 and 4.

10. What is the probability that a blood sample from a normal person would have fewer than 10 red blood cells?

11. What is the probability that a blood sample from a normal person will have at least 15 red blood cells? HINT: Since there is no theoretical upper limit to the Poisson distribution, the correct way to answer this question is to calculate 1 – probability of fewer than 15 red blood cells. ASSIGNMENT 3 20 INTRODUCTORY STATISTICS LABORATORY

12. A person with a red blood cell count in the lower 2.5 percent of the distribution might be considered as deficient. What is the red blood cell count below which 2.5 percent of the distribution lies? HINT: You need to determine a value X so that if you sum all the probabilities for counts up to and including that value they will sum to at least 0.025. The sum of probabilities of all counts up to but excluding X should be less than 0.025. You can proceed in the following way. Look at the table to guess how many probabilities (P[X = 0] + P[X = 1] + . . ) should be added to give a sum of approximately 0.025. Calculate sums of probabilities for your guess of X. Continue your guessing of X until you get a sum ≥ 0.025 while the sum for X-1 < 0.025.

13. What is the mean red blood cell count in this distribution?

14. What is the variance of red blood cell count in this distribution? HINT: See question 7, and remember it is a Poisson distribution.

15. Is the following statement true (1) or false (0) for this distribution? In a Poisson distribution, the variance is equal to the mean (within rounding error). Record 1 if true, 0 if false.

6. For each of the scenarios below, identify the sampling blunder, speculate about the influence of the bias, and then make a recommendation for ridding the study of the biasing influence. a. A researcher wanted to know how people in the local community felt about the use of high-stakes testing in the public schools. The researcher spent the afternoon at Wal-Mart and randomly approached 100 shoppers to ask their opinion (they all agreed to cooperate). Random selection was accomplished with the use of a random number table (the numbers determined which shopper to target, such as the 16th to exit, then the 30th to exit, then the ninth to exit, etc.). b. A researcher wanted to know how students at a university felt about mandatory fees for all students to support a child care center for students with children. The researcher set up a table near the dormitory where many different types of students came and went. Those who stopped at the table and seemed friendly were asked to complete the questionnaire. c. To study differences in occupational aspirations between Catholic high school students and public high school students, a researcher randomly sampled (using school rosters and a random number table) 200 students from the largest Catholic high school and the largest public high school. d. To learn more about teachers' feelings about their personal safety while at school, a questionnaire was printed in a nationwide subscription journal of interest to many teachers. Teachers were asked to complete the questionnaire and mail it (postage paid) to the journal headquarters for tabulation. e. To study the factors that lead teachers in general to quit the profession, a group of teachers threatening to quit was extensively interviewed. The researcher obtained the group after placing an announcement about the study on the teachers' bulletin board at a large elementary school.

Explain ANOVA (Analysis of Variance). How is F test for differences among more than two means used in this case to test a hypothesis? Give an example.