Kay listens to either classical or country music every day while she works. If she listens to classical music one day, there is a 66% chance that she will listen to country music the next day. If she listens to country music, there is a 77% that she will listen to classical music the next day.

(a) If she listens to country music on Monday, what is the probability she will listen to country music on Thursday?

All of the same information about Kay's listening habits remain true. However, suppose you know the additional fact that on a particular Monday the probability that she is listening to classical music is 0.24.

(b) Based on your additional knowledge that there is a 0.24 probability that she is listening to classical music on Monday, what is the probability she will be listening to country music on Wednesday?

(c) Based on your additional knowledge that there is a 0.24 probability that she is listening to classical music on Monday, what is the probability that she will be listening to classical music on Thursday?

Every morning Mary randomly decides on one of three possible ways to get to work. She makes her choice so that all three choices are equally likely. The three choices are described as follows: • Choice A (Drives the highway): The highway has no traffic lights but has the possibility of accidents. The number of accidents on the highway for the hour preceding Mary’s trip, X, follows a Poisson distribution with an average of 2. The time (minutes) it takes her to get to work is affected by the number of accidents in the hour preceding her trip due to clean up. The time (in minutes) it takes her is given by T = 54.5 + 5X. • Choice B (Drives through town): Suppose there is no possibility of being slowed down by accidents while going through town. However, going through town she must pass through 10 traffic lights. Suppose all traffic lights act independently from one another and for each there is a probability of 0.5 that she will have to stop and wait (because it is red). Let Y be the number of lights she will stop and wait at. The time (in minutes) it takes her is given by T = 58.5 + Y. • Choice C (Takes the train): Trains arrive for pick-up every 5 minutes. If the train has room, it will take her exactly 50 minutes to get to work. If an arriving train is full she will have to wait an additional 5 minutes until the next train arrives. Trains going through the station will arrive full with probability 0.75, and thus she cannot get on and will have to wait until the next train. Suppose it takes Mary exactly 5 minutes to get to the train station and she always arrives at the station just as a train arrives. Let Z be the number of trains she’ll see until she can finally board (the train isn’t full). The time (in minutes) it takes her is given by T = 50 + 5Z.

a) Which choice should she make every morning to minimize her expected travel time?

b) On one morning Mary starts her journey to work at 7am. Suppose it is necessary that she is at work at or before 8:00 am. Which route should she take to maximize the probability that she is at work at or before 8:00am?

5.34 Number of friends on Facebook. To commemorate Facebook’s 10-year milestone, Pew Research reported several facts about Facebook obtained from its Internet Project survey. One was that the average adult user of Facebook has 338 friends. This population distribution takes only integer values, so it is certainly not Normal. It is also highly skewed to the right, with a reported median of 200 friends. 8 Suppose that σ = 380 and you take an SRS of 80 adult Facebook users. For your sample, what are the mean and standard deviation of x ¯, the mean number of friends per adult user? Use the central limit theorem to find the probability that the average number of friends for 80 Facebook users is greater than 350.

In a certain state lottery, a lottery ticket costs $1. In terms of the decision to purchase or not to purchase a lottery ticket, suppose that the following payoff table applies:

1. A realistic estimate of the chances of winning is 1 in 260,000. Use the expected value approach to recommend a decision. If required, round your answer to two decimal places. If the amount is zero enter “0”.
   
   Recommended decision: Purchase Lottery Ticket  
   
   Expected Value = $  
   
2. If a particular decision maker assigns an indifference probability of 0.00001 to the $0 payoff. Would this individual purchase a lottery ticket?
   
   Decision: Yes, Purchase Lottery Ticket  
   
   Use expected utility to justify your answer. If required, round your answer to five decimal places.
   
   Expected Utility =  
   
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
   

1. In an instant lottery, your chances of winning are 0.1. If you play the lottery six times and outcomes are independent, determine the probability that

(i) you win at most once.

(ii) you lose all six times.

(iii) you win exactly two times.

Please show work will rate!!!

A.) A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the cable can hold. The weight limit will be reported on cable packaging. The engineers take a random sample of 43 cables and apply weights to each of them until they break. The 43 cables have a mean breaking weight of 774.3 lb. The standard deviation of the breaking weight for the sample is 15.4 lb.

Find the 90% confidence interval to estimate the mean breaking weight for this type cable.

( _______,____________ )

Your answer should be rounded to 2 decimal places.

B.)

According to the website www.collegedrinkingprevention.gov, “About 25 percent of college students report academic consequences of their drinking including missing class, falling behind, doing poorly on exams or papers, and receiving lower grades overall.” A statistics student is curious about drinking habits of students at his college. He wants to estimate the mean number of alcoholic drinks consumed each week by students at his college. He plans to use a 90% confidence interval. He surveys a random sample of 50 students. The sample mean is 3.90 alcoholic drinks per week. The sample standard deviation is 3.51 drinks.

Construct the 90% confidence interval to estimate the average number of alcoholic drinks consumed each week by students at this college.

( ______, ________ )

Your answer should be rounded to 2 decimal places.

The following data is from a survey that was conducted in both 1996 and 2001. Did the rates of smoking differ from 1996 to 2001? *Smokers are defined as those who smoke every day. (Data from WSJ,

1. A sociologist claims that children ages 6-17 spend less time watching television today than children ages 6-17 in 200 1 did. A study was conducted recently and a similar study was conducted in 2001. The results are given below:

Recently 2001

Mean amount of time ( hours per weekday) 1.76 2.13

Sample standard deviation 0.47 0.49

Sample Size 40 35

a. Test the claim of the sociologist at 10% level of significance.

Use classical approach and label all steps clearly

b. Test the claim of the sociologist at 10% level of

significance. Use P-value method and label all steps clearly

Which correlation coefficient is the most appropriate for measuring the relationship between Right/ Left Handedness and Reading Comprehension Scores?

A. Spearman Rho

B. chisquare

C. phi coefficient

D. point biserial

How do you choose between Spearman Rho and Point Biserial? I am stuck between these two answers.

Simulate the effect of the Price change if it will follow the following pattern for Type A. (build the 95% confidence interval) Type A (Price (million Dollar) =1.25 (20% probability); Price (million Dollar) =2.25 (40 % probability); Price (million Dollar) =3 (25 % probability); Price (million Dollar) =3.5 (15 % probability))

9A A personnel researcher has designed a questionnaire and she would like to estimate the average time to complete the questionnaire. Suppose she samples 100 employees and finds that the mean time to take the test is 27 minutes with a standard deviation of 4 minutes. Construct a 90% confidence interval for the mean time to complete the questionnaire. Also, write a short explanation about the findings to the human resources director of your company summarizing the results. – Use Excel for this analysis.

9B. For the problem in part A, the human resources director wants to know whether these is sufficient sample evidence to conclude that the average time to complete the questionnaire is not 27 minutes. Set up the hypotheses (in statistical terms) and, based only on the confidence interval you have constructed in part A, what would you conclude regarding the hypotheses?

H0 :

H1 :

In a study conducted to investigate browsing activity by shoppers, each shopper was initially classified as a nonbrowser, light browser, or heavy browser. For each shopper, the study obtained a measure to determine how comfortable the shopper was in a store. Higher scores indicated greater comfort. Suppose the following data were collected.

a. Use a= .05 to test for a difference among mean comfort scores for the three types of browsers.

Compute the values identified below (to 2 decimals, if necessary).

Calculate the value of the test statistic (to 2 decimals, if necessary).

b. Use Fisher's LSD procedure to compare the comfort levels of nonbrowsers and light browsers. Use a= .05 .

Compute the LSD critical value (to 2 decimals).

A psychologist believes that students’ test scores will be affected if they have too much caffeine before taking an exam. To examine this, she has a sample of n = 15 students drink five cups of coffee before taking an exam. She uses an exam that has a population mean of µ = 72 and a population standard deviation s = 3. The mean test score for the sample of 15 students who drank five cups of coffee before taking the exam was M = 69. Do a t-test using a = .01 a. Is this a one-tailed test or a two-tailed test? (circle one) b. What is the research hypothesis, H1? c. What is the null hypothesis, H0? d. Calculate the degrees of freedom (df) for this problem. e. From the t-distribution table (B.2), what is the critical value of tcrit for a = .01? f. Calculate the mean of the distribution of sample means, µM g. Calculate the standard error of the mean, sM h. Calculate the t-score of the sample mean. i. Sketch the distribution of sample means. Indicate where the sample mean is, where the critical value of t is, and the area under the tail of the curve. j. Can you reject the null hypothesis, H0? YES or NO (circle one) k. Can you accept the research hypothesis, H1? YES or NO (circle one)

The output of a chemical process is monitored by taking a sample of 20 vials to determine the level of impurities. The desired mean level of impurities is 0.048 grains per vial. If the mean level of impurities in the sample is too high, the process will be stopped and purged; if the sample mean is too low, the process will be stopped and the values will be readjusted. Otherwise, the process will continue.
a)  Sample results provide sample mean to be equal to 0.057 gram with sample standard deviation equal to 0.018. At a significance level of 0.01, should the process be stopped? If so, what type of remedial action will be required?
b)  Assume that the mean level of impurities is within tolerable limits. If the maximum tolerable variability of the process is 0.0002, do the sample results verify the suspicion that the maximum tolerable variability has been exceeded? Use a 5% level of significance.

Why are sampling distributions important to the study of inferential statistics? In your answer, demonstrate your understanding by providing an example of a sampling distribution from an area such as business, sports, medicine, social science, or another area with which you are familiar. Remember to cite your resources and use your own words in your explanation.