The quality control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7,500 hours. The population standard deviation is 1,200 hours. A random sample of 64 CFLs indicates a sample mean life of 7,250 hours.

a. At the 0.05 level of significance, is there evidence that the mean life is different from 7,500 hours?

b. Compute the p-value and interpret its meaning.

c. Construct a 95% confidence interval estimate of the population mean life of the CFLs.

d. Compare the results of (a) and (c). What conclusions do you reach?

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Consider the following statistical studies. Which method of data collection would likely be used to collect data for each study? Explain your selection. What is the population of interest?

Would you take a census or use a sampling? Explain. If you would use a sampling, decide what type of sampling technique you would use. Explain your reasoning.

1. A study of the effect of exercise on relieving depression.

2. A study of the success of graduates of a large university in finding a job within one year of graduation.

3. A study of how often people wash their hands in public restrooms.

describe how the presence of possible outliers might be identified on
histograms
dotplots
stem-and-leaf displays
box-and-whisker plots

21. Bob’s local pizza place claims it delivers pizzas in 30 minutes on average. Bob is convinced it’s more than that. He does a hypothesis test and gets a p-value of .001.

a. What does Bob conclude?

b. If Bob made the wrong conclusion what error did he make?

c. What would be the impact of his error?

22. Bob’s local pizza place claims it delivers pizzas in 30 minutes on average. Bob is convinced it’s more than that. He does a hypothesis test and gets a p-value of .10.

a. What does Bob conclude?

b. If Bob made the wrong conclusion what error did he make?

c. What would be the impact of his error?

23. Which type of error is the same as the significance level of a hypothesis test?

a. Type 1 error

b. Type 2 error

c. Both

d. Neither

Periodically, Merrill Lynch customers are asked to evaluate Merrill Lynch financial consultants and services (2000 Merrill Lynch Client Satisfaction Survey). Higher ratings on the client satisfaction survey indicate better service with 7 the maximum service rating. Independent samples of service ratings for two financial consultants are summarized here. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. Use = .05 and test to see whether the consultant with more experience has the higher population mean service rating. Consultant A n=16, x1=6.82, s1= 0.64 Consultant B= N2=10, X2=6.25, S2=0.75   

Compute the value of the test statistic (to 2 decimals).

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))