(All answers were generated using 1,000 trials and native Excel functionality.)

Grear Tire Company has produced a new tire with an estimated mean lifetime mileage of 36,500 miles. Management also believes that the standard deviation is 5,000 miles and that tire mileage is normally distributed. To promote the new tire, Grear has offered to refund some money if the tire fails to reach 30,000 miles before the tire needs to be replaced. Specifically, for tires with a lifetime below 30,000 miles, Grear will refund a customer $1 per 100 miles short of 30,000.

1a)State two advantages of Bayesian data analysis over a classical approach?

1b)Explain why one would need a sensitivity analysis on the choice of prior distribution ?.

1. Objectives:

1) Select a simple random sample by random number table or Excel.

2) Know the sampling distribution of and, and calculate the probabilities by excel.

Q1: The director of personnel for Electronics Associates, Inc (EAI), has been assigned the task of developing a profile of the company’s 250 managers. The characteristics to be identified include the mean annual salary for the managers and the proportion of managers have completed the company’s management training program. Using the 2500 managers as the population for this study. (See data in a file named EAI).

Select a simple random sample of 30 managers from the 2500 EAI managers.

Q2: Business Weej conducted a survey of graduates from 30 top MBA programs (Business-Week, September 22, 2003). On the basis of the survey, assume that the mean annual salary for male and female graduates 10 years after graduation is $168,000 and $117,000, respectively. Assume the standard deviation for the male graduates is $40,000, and for the female graduates, it is $25,000.

a. What is the probability that a simple random sample of 40 male graduates will provide a sample mean within $10,000 of the population mean, $168,000?

b. What is the probability that a simple random sample of 40 female graduates will provide a sample mean within $10,000 of the population mean, $117,000?

c. In which of the preceding two cases, part (a) and part (b), do we have a higher probability of obtaining a sample estimate within $10,000 of the population mean? Comment on the results.

Q3: The Grocery Manufacturers of America reported that 76% of consumers read the ingredients listed on a product’s label. Assume the population proportion p=0.76, and a sample of 400 consumers is selected from the population.

a. Show the sampling distribution of the sample proportion, where is the proportion of the sampled consumers who read the ingredients listed on a product’s label.

b. What is the probability that the sample proportion will be within +- 0.03 of the population proportion?

c. Answer part (b) for a sample of 750 consumers.

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 7.505 hours. The population standard deviation is 100 hours. A random sample of 64 light bulbs indicates a sample mean life of 7.480 hours.

a. At the 0.05 level of significance, is there evidence that the mean life is different from 7.505 hours?

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

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

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

In a group of 14 young professionals studied, it was found that they purchased on average $171.719 per month eating meals prepared outside the home, with a standard deviation of $36.011. What is the 90% confidence interval of the true amount of money young professionals spend monthly on meals prepared outside the home?

Question 3 options:

I'm a little confused regarding types of data & measurement scales for statistics, including: Nominal, Ordinal, Interval and Ratio.

If one were to categorize class standing, (1=freshmen, 2=sophomore, 3=junior and 4=Senior) would this be considered Nominal, Ordinal or interval? and why?

A rehabilitation center researcher was interested in examining the relationship between physical fitness prior to surgery of persons undergoing corrective knee surgery and time required in physical therapy until successful rehabilitation. Patient records in the rehabilitation center were examined, and 24 male subjects ranging in age from 18 to 30 years who had undergone similar corrective knee surgery during the past year were selected for the study. The number of days required for successful completion of physical therapy and the prior physical fitness status (below average, average, above average) for each patient follow.

1. Explore the with side-by-side box-plots. Discuss the results of your graphical exploration.
2. Calculate group mean and standard deviation.
3. Complete a one-way analysis of variance for this problem. Show all hypothesis-testing steps and interpret the results.

(1 point) The distribution of actual weights of 8-oz chocolate bars produced by a certain machine is normal with mean 8 ounces and standard deviation 0.13 ounces.

(a) What is the probability that the average weight of a bar in a Simple Random Sample (SRS) with three of these chocolate bars is between 7.9 and 8.16 ounces? ANSWER:

(b) For a SRS of three of these chocolate bars, what is the level L such that there is a 4% chance that the average weight is less than L? ANSWER:

How do I do these computations without a normal distribution chart and just a TI84 calculator?

6.7 Given a standard normal distribution, find the value of k such that

(a) P(Z>k)=0 .2946;

(b) P(Z<k)=0 .0427;

(c) P(−0.93 <Z<k)=0 .7235.

6.8 Given a normal distribution with μ = 30 and σ = 6, find

(a) the normal curve area to the right of x = 17;

(b) the normal curve area to the left of x = 22;

(c) the normal curve area between x = 32 and x = 41;

(d) the value of x that has 80% of the normal curve area to the left;

(e) the two values of x that contain the middle 75% of the normal curve area.

A person’s muscle mass is expected to be associated with age. Some people also thought exercise time would be associated with the muscle mass. To explore the potential relationships between muscle mass and age, muscle mass and exercise time, a nutritionist randomly selected 20 women from a population of women with age ranging from 40 to 80 years old, and measured their muscle mass (a score without unit) and exercise time (hours per month)

What do the two regression parameters (b0 and b1) mean?

1)Your master's dissertation concerns recent immigrants' experiences of severe financial strain. A large sample of 960 residents of a medium-sized city indicated that 80% of new immigrants felt that they were extremely stressed financially (which was higher than what is average for the general population). If you were to construct a 99% confidence interval for your finding, what would be the LOWER LIMIT of the interval? (Write as a proportion to 3 decimal places, rather than a percentage)

2) This question is similar to EOC 7.34. Your master's dissertation concerns recent immigrants' experiences of severe financial strain. A large sample of 960 residents of a medium-sized city indicated that 80% of new immigrants felt that they were extremely stressed financially (which was higher than what is average for the general population.) If you were to construct a 99% confidence interval for your finding, what would be the UPPER LIMIT of the interval (written as a proportion to 3 decimal places, rather than a percentage)?

A manufacturer claims that the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor. A sample of 9 phones from the manufacturer had a mean range of 1180 feet with a standard deviation of 35 feet. A sample of 15 similar phones from its competitor had a mean range of 1120 feet with a standard deviation of 20 feet. Do the results support the manufacturer's claim? Let μ1 be the true mean range of the manufacturer's cordless telephone and μ2 be the true mean range of the competitor's cordless telephone. Use a significance level of α=0.1 for the test. Assume that the population variances are equal and that the two populations are normally distributed.

Step 2 of 4 : Compute the value of the t test statistic. Round your answer to three decimal places.

Step 1 of 4: State the null and alternative hypotheses for the test.

Step 2 of 4: Compute the value of the t test statistic. Round your answer to three decimal places. Step 3 of 4: Determine the decision rule for rejecting the null hypothesis H0. Round your answer to three decimal places.

Step 4 of 4: State the test's conclusion.

Calculate the average value of the numbers 3, 3, 5, 5 first by calculating the normal average and then by calculating the weighted average. Are the two results the same?

Populations may be _____________ or ________________________. A real population is one in which all observations are ______________________________ at the time of sampling. A hypothetical population is one in which all observations are _____________________________ at the time of ___________________. Often it is not convenient or even possible to include all observations in a research project. In such cases, a _____________________ or subset of observations is taken. The size of the sample is partially determined by estimated ___________________________among observations and by an acceptable amount of _______________________. In order to use inferential statistics, the analysis must be based on a ____________________ sample. A sample is random, if at each stage of the sampling, the selection process guarantees that all remaining __________________ have ____________________ chances of being selected. The observations in a randomly selected sample should be ___________________ of those in the population. However, there is no guarantee of this. The term random describes the process, and not necessarily the outcome. One of the best-known techniques for selecting a random sample is the ________________ method. All observations must be represented on slips of paper that are deposited in a bowl and _________________. The through stirring is a very important aspect of this method of sample selection. Another method for generating a random sample involves the use of the table of ____________ numbers. When using this table, the number of digits actually used is determined by the ____________ __________________. This method is not very efficient for obtaining a sample from a ____________ population. In an experiment, although subjects may not be selected randomly, they should be randomly assigned to either the experimental or control condition. The purpose of random assignment is to make sure that, except for __________________ differences, groups of subjects are similar with respect to any ____________________________________________. It is usually desirable that _____________ numbers of subjects be assigned to the experimental and control groups. To accomplish this, assignment should be done in ______________________.