Exam 20: Probability and Combinatorics

Which of the following is not true about business analytics?

The changes in the price of the least consumed commodities are overly influential in a weighted aggregate price index.

SCENARIO 5-12 Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants. Your profit (in thousands of dollars) will depend on the taste of the consumers when winter arrives. The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table. Probability Taste Design A Design B 0.2 more conservative 180 520 0.5 no change 230 310 0.3 more liberal 350 270 -Referring to Scenario 5-12, if you decide to choose Design A for half of the production lines and Design B for the other half, what is the risk of your investment?

A debate team of 4 is to be chosen from a class of 35. There are two twin brothers in the class. How many possible ways can the team be formed which will include both of the twin brothers?

To construct bootstrap confidence interval estimate for the population mean with confidence level $( 1 - \alpha )$ 100% , you will order the resampled means for the m samples that you have drawn from the initial sample of size n, use the value of the resampled mean that cuts off the smallest ?/ 2×100% as the lower limit and the value of that cuts off the largest ?/ 2×100% as the upper limit.

SCENARIO 12-20 The director of the MBA program of a state university wanted to know if a one week orientation would change the proportion among potential incoming students who would perceive the program as being good. Given below is the result from 215 students' view of the program before and after the orientation. -Referring to Scenario 12-20, the director should reject the null hypothesis using a 1% level of significance.

Eleven freshmen are to be assigned to eleven empty rooms in a student dormitory. Each room is considered unique so that it matters who is being assigned to which room. How many different ways can those eleven freshmen be allocated?

SCENARIO 16-17 Given below are the prices of a basket of four food items from 2008 to 2012. Year Wheat( \/ Bushel) Corn( \/ Bushel) Soybeans( \/ Bushel) Milk( \/ hundredweight) 2008 4.25 3.71 7.41 15.03 2009 3.43 2.7 7.55 13.63 2010 2.63 2.3 6.05 15.18 2011 2.11 1.97 4.68 14.72 2012 2.16 1.9 4.81 12.32 -Referring to Scenario 16-17, what is the Paasche price index for the basket of four food items in 2012 that consisted of 40 bushels of wheat, 50 bushels of corn, 35 bushels of soybeans and 60 hundredweight of milk in 2012 using 2008 as the base year?

To determine the probability of getting no more than 3 events of interest in a binomial distribution, you will find the area under the normal curve for X = 2.5 and below.

As a general rule, one can use the normal distribution to approximate a binomial distribution whenever $n ( \pi - 1 )$ is at least 5.

SCENARIO 8-15 A wealthy real estate investor wants to decide whether it is a good investment to build a high-end shopping complex in a suburban county in Chicago. His main concern is the total market value of the 3,605 houses in the suburban county. He commissioned a statistical consulting group to take a sample of 200 houses and obtained a sample mean market price of $225,000 and a sample standard deviation of $38,700. The consulting group also found out that the mean differences between market prices and appraised prices was $125,000 with a standard deviation of $3,400. Also the proportion of houses in the sample that are appraised for higher than the market prices is 0.24. -Referring to Scenario 8-15, what will be the 90% confidence interval for the total market price of the houses in the suburban county constructed by the consulting group?

SCENARIO 11-11 An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants all 3 varieties of the seeds on each of 5 different patches of fields. She then measures the crop yield in bushels per acre. Treating this as a randomized block design, the results are presented in the table that follows. 1 11.1 19.0 14.6 2 13.5 18.0 15.7 3 15.3 19.8 16.8 4 14.6 19.6 16.7 5 9.8 16.6 15.2 -Referring to Scenario 11-11, what is the p-value of the test statistic for the randomized block F test for the difference in the means?

SCENARIO 6-8 A company has 125 personal computers. The probability that any one of them will require repair on a given day is 0.15. -Referring to Scenario 6-8 and assuming that the number of computers that requires repair on a given day follows a binomial distribution, compute the probability that there will be more than 25 but less than 30 computers that require repair on a given day using a normal approximation.

SCENARIO 5-12 Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants. Your profit (in thousands of dollars) will depend on the taste of the consumers when winter arrives. The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table. Probability Taste Design A Design B 0.2 more conservative 180 520 0.5 no change 230 310 0.3 more liberal 350 270 -Referring to Scenario 5-12, if your investment preference is to maximize your expected profit and not worry at all about the risk that you have to take, will you choose a production mix that will consist of 10%, 30%, 50%, 70%, or 90% of your production lines for Design A and the remaining for Design B?

SCENARIO 11-12 A student team in a business statistics course designed an experiment to investigate whether the brand of bubblegum used affected the size of bubbles they could blow. To reduce the person-to-person variability, the students decided to use a randomized block design using themselves as blocks. Four brands of bubblegum were tested. A student chewed two pieces of a brand of gum and then blew a bubble, attempting to make it as big as possible. Another student measured the diameter of the bubble at its biggest point. The following table gives the diameters of the bubbles (in inches) for the 16 observations. -Referring to Scenario 11-12, the among-block variation or SSBL is __________.

SCENARIO 5-13 From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed. -Referring to Scenario 5-13, what is the probability out of the 8 new cars it just received that, when each is tested, at least half of the cars have defective radios?

SCENARIO 9-12 A drug company is considering marketing a new local anesthetic. The effective time of the anesthetic the drug company is currently producing has a normal distribution with a mean of 7.4 minutes with a standard deviation of 1.2 minutes. The chemistry of the new anesthetic is such that the effective time should be normally distributed with the same standard deviation. The company will market the new local anesthetic as being better if there is evidence that the population mean effective time is greater than the 7.4 minutes of the current local anesthetic. -Referring to Scenario 9-12, if you select a sample of 25 new local anesthetics and are willing to have a level of significance of 0.05, the probability of the company incorrectly marketing the new local anesthetic when it is not better is _____.

"Big data" is a concrete concept with a precise operational definition.

SCENARIO 11-11 An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants all 3 varieties of the seeds on each of 5 different patches of fields. She then measures the crop yield in bushels per acre. Treating this as a randomized block design, the results are presented in the table that follows. 1 11.1 19.0 14.6 2 13.5 18.0 15.7 3 15.3 19.8 16.8 4 14.6 19.6 16.7 5 9.8 16.6 15.2 -Referring to Scenario 11-11, the null hypothesis for the F test for the block effects should be rejected at a 0.01 level of significance.

SCENARIO 4-10 Are whites more likely to claim bias? It was found that 60% of the workers were white, 30% were black and 10% are other races. Given that a worker was white, the probability that the worker had claimed bias was 30%. Given that a worker was black, the probability that the worker had claimed bias was 40%. Given that a worker was other race, the probability that the worker had claimed bias was 0%. -Referring to Scenario 4-10, if a randomly selected worker had not claimed bias, what is the probability that the worker is white?