The following is the transition probability matrix of a Markov chain with states 1, 2, 3, 4 P

If Xnot = 1
(a) find the probability that state 3 is entered before state 4;

(b) find the mean number of transitions until either state 3 or state 4 is entered.

19. Researchers believe that a higher percentage of males are afflicted with cysturina than females. Suppose of the 50 individuals, 15 were females and the remainder were males. Using 99% confidence, estimate the proportion of females with cysturina. Then estimate the proportion of females afflicted with cysturina at 96% confidence.

Up to 20% of Americans contract influenza each year. A sample of 400 randomly selected Americans is chosen and the number with influenza is recorded. Let X represent the number with influenza in the sample. What is the probability that, at most, 25% of the sample is observed to have influenza? How can I do this the easiest way on Ti-84? Can I use a button like Stats or Distr to make life easy?

Students attending a certain university can select from 130 major areas of study. A student's major is identified in the registrar's records with a two-or three-letter code (for example, statistics majors are identified by STA, math majors by MS). Some students opt for a double major and complete the requirements for both of the major areas before graduation. The registrar was asked to consider assigning these double majors a distinct two- or three-letter code so that they could be identified through the student records system.

(a)

What is the maximum number of possible double majors available to the university's students?

double majors

(b)

If any two- or three-letter code is available to identify majors or double majors, how many major codes are available?

codes

(c)

How many major codes are required to identify students who have either a single major or a double major?

codes

(d)

Are there enough major codes available to identify all single and double majors at the university?

Yes

No    

A professor takes a random sample of 25 students and administers a test with questions increasing in difficulty. He takes another sample of 25 students and administers a test with questions decreasing in difficulty. He records measures of test anxiety based on a scale from 1 to 10 (most anxious). Using steps below, run an F test to test the claim that the two given samples come from populations with different variances. Use α = 0.01.

A. State the null and alternative hypotheses in terms of σ₁² & σ₂². Be sure to label which population is which.

B. Find the critical value, Test statistic, and P-value

C. Decision? Reject / Fail to Reject

D. Are the two given samples from populations with different variances? yes/no

Use R to compute the probability that a Normal random variable with mean 0 and variance 3.7 is less than.2. Find the 93% quantile of the above random variable by using the R command and also by using the z -table.

How do you test if there is evidence of a relationship between two things? Which statistically test would need to be used?

****URGENT******

1A)  An event has four possible outcomes, A, B, C, and D. All of the outcomes are disjoint.

Given that P(B^c) = 0.2, P(A) = 0.1, and P(C) = 0.3, what is P(D)?

1B) A study was conducted on a potential association between drinking coffee and being diagnosed with clinical depression. All 18,832 subjects were female. The women were free of depression at the start of the study in 1996. Information was collected on coffee consumption and the incidence of clinical depression during the ten-year study period.

Are the following events independent?

Event LC: The event of drinking less than or equal to 1 cup of coffee per week

(Little Coffee = LC)

Event D: The event of a diagnosis of clinical depression

(Depression = D)

Round your calculations to four decimal places (or fewer) at each step.

There are multiple ways to test for independence. All involve the comparison of observed and expected probabilities based on probability theory.

In this context:

If the two probabilities are similar (identical to two decimal places), this is evidence of independence.

If the two probabilities are not similar (not identical to two decimal places), this is evidence of a lack of independence.

C) What do your results in (b) tell us, about the ways in which drinking very little coffee (0-1 cups per week) influences, or does not influence, the probability of depression for women in the study population?

Write a R-script to (and show the outputs of your code)

(a) Create a sequence of numbers starting at 3.5 and ending at 10.7 with increments of 0.79. Find the variance and mean of those numbers. And finally sort the vector in a decreasing manner

(b) Create a 3 different 3 by 3 matrices such that each of the numbers 1,2,...,9 appear exactly once (Sudoku style) in each of the matrices.

A random sample with replacement of size 100 is drawn from a population with mean 3.5 and standard deviation 3. Use the normal approximation to calculate the probability that the sample average is between 3 and 4. Round your answer to three decimal places.

Scenario 8.2

The undergraduate grade point average (GPA) for students admitted to the top graduate business schools was 3.37. Assume this estimate was based on a sample of 90 students admitted to the top schools. Using past years' data, the population standard deviation can be assumed known as 0.30.  

1. Based on the information in Scenario 8.2, you are to construct a 95% confidence interval estimate of the mean undergraduate GPA for students admitted to the top graduate business schools, that is
[ Lower limit , Upper limit ].

The Lower limit of this 95% confidence interval is equal to ? (to 2 decimals)?

2. Based on the information in Scenario 8.2, you are to construct a 95% confidence interval estimate of the mean undergraduate GPA for students admitted to the top graduate business schools, that is
[ Lower limit , Upper limit ].

The Upper limit of this 95% confidence interval is equal to ? (to 2 decimals)?

Correlation - Do you think there would be a positive correlation between a placement test score and the final grade in this statistics class? What other variables do you think would have a positive correlation with the final grade in this (or any) class? What variables would have a negative correlation with a final grade in a class? Look up a study that finds a correlation between grades and some other variable. Describe the variables, the study, the methods used, whether the correlation is positive or negative, and how this relates to your life.

A researcher tested a research hypothesis that people with diagnosed depression will have REDUCED level of depressive symptoms after a cognitive therapy treatment, as compared to the pre-treatment level of depressive symptoms. The cutoff t value is -1.833 for this one-tailed test. The data analysis yielded a mean change score (post-treatment minus pre-treatment) of -2.5. If the standard error is 2.0, what is the t statistic and what is the conclusion of the hypothesis test?

A researcher conducts a t test for dependent means (paired-samples t test) with 16 participants. The estimated population variance of the change scores is 9. What is the standard error?

In a small-scale trial (sample size = 9) of a psychotherapy treatment for depression, participants were assessed with a depression scale when they entered the trial and again when they have completed the 6-month trial. The data yielded a mean difference (change) score of 1.5 and the standard deviation of the sampling distribution was .6. What was the the t statistic?

In a high school math class, there are 13 male students and 17 female students. After all the students have taken the ACT test, the math teacher would like to know if there is a significant difference in the math component score between the male and female students. If he uses an alpha level of .05 for a two-tailed test, what would be the critical t value for his statistical test?

suppose given the three pairwise independent events, all three of which cannot simultaneously occur. Assuming that they all have the same probability x , determine the largest possible value of x.

Sometimes probability statements are expressed in terms of odds. The odds in favor of an event A are the following ratio.

P(A)/P(not A) = P(A)/P(Ac)

For instance, if P(A) = 0.60, then P(Ac) = 0.40 and the odds in favor of A are 0.60/ 0.40 = 6/4 = 3/2 , written as 3 to 2 or 3:2.

(a) Show that if we are given the odds in favor of event A as n:m, the probability of event A is given by the following. P(A) = n/n + m Hint: Solve the following equation for P(A). n/m = P(A)/1 − P(A)

n(1 − P(A)) = _____ (P(A))

n − nP(A) = ____P(A)

n = ____P(A) + nP(A)

n =_____ P(A)

n/n + m = P(A)

(b) A telemarketing supervisor tells a new worker that the odds of making a sale on a single call are 6 to 19. What is the probability of a successful call? (Round your answer to two decimal places.)

(c) A sports announcer says that the odds a basketball player will make a free throw shot are 3 to 5. What is the probability the player will make the shot? (Round your answer to two decimal places.)

When do creative people get their best ideas? USA Today did a survey of 966 inventors (who hold U.S. patents) and obtained the following information.

(a) Assuming that the time interval includes the left limit and all the times up to but not including the right limit, estimate the probability that an inventor has a best idea during each time interval: from 6 A.M. to 12 noon, from 12 noon to 6 P.M., from 6 P.M. to 12 midnight, from 12 midnight to 6 A.M. (Enter your answers to 3 decimal places.)

John runs a computer software store. Yesterday he counted 123 people who walked by the store, 52 of whom came into the store. Of the 52, only 23 bought something in the store. (Round your answers to two decimal places.)

(a) Estimate the probability that a person who walks by the store will enter the store.


(b) Estimate the probability that a person who walks into the store will buy something.


(c) Estimate the probability that a person who walks by the store will come in and buy something.


(d) Estimate the probability that a person who comes into the store will buy nothing.