Exam 20: Probability and Combinatorics

Using the number of registered voters who turned out to vote for the primary in Iowa to predict the number of registered voters who will turn out to vote in Vermont's primary is an example of descriptive statistics.

SCENARIO 4-15 At a Texas college, 60% of the students are from the southern part of the state, 30% are from the northern part of the state, and the remaining 10% are from out-of-state. All students must take and pass an Entry Level Math (ELM) test. 60% of the southerners have passed the ELM, 70% of the northerners have passed the ELM, and 90% of the out-of-staters have passed the ELM. -Referring to Scenario 4-15, if a randomly selected student has not passed the ELM, the probability the student is from southern Texas is ________.

SCENARIO 9-13 A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly. Based on past experience, the population standard deviation is 50 hours and the light bulb life is normally distributed. The operations manager stops the production process if there is evidence that the population mean light bulb life is below 500 hours. -Referring to Scenario 9-13, if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.10, the power of the test is _____ if the population mean bulb life is 490 hours.

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 0.01, the probability of the company incorrectly marketing the new local anesthetic when its population mean effective time is not greater than the 7.4 minutes is _____.

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 minimize the amount of risk that you have to take and do not care at all about the expected profit, 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?

A debate team of 4 members for a high school will be chosen randomly from a potential group of 15 students. Ten of the 15 students have no prior competition experience while the others have some degree of experience. What is the probability that none of the members chosen for the team have any competition experience?

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, what is the critical value of the randomized block F test for the difference in the means at a level of significance of 0.05?

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, what is the p-value of the test statistic for the randomized block F test for the difference in the means?

SCENARIO 9-14 An appliance manufacturer claims to have developed a compact microwave oven that consumes a population mean of no more than 250 W. From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W. If there is evidence that the population mean consumption is greater than 250 W, the manufacturer will be unable to make the claim. -Referring to Scenario 9-14, if you select a sample of 20 compact microwave ovens and are willing to have a level of significance of 0.10, the power of the test is _____ if the mean power consumption of all such microwave ovens is in fact 248 W.

SCENARIO 5-14 An accounting firm in a college town usually recruits employees from two of the universities in town. This year, there are fifteen graduates from University A and five from University B and the firm decides to hire six new employees from the two universities. -Referring to Scenario 5-14, what is the probability that all six of the new employees will be from University A?

A debate team of 4 members for a high school will be chosen randomly from a potential group of 15 students. Ten of the 15 students have no prior competition experience while the others have some degree of experience. What is the probability that at least 1 of the members chosen for the team have some prior competition experience?

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 amount of total variation or SST is __________.

SCENARIO 8-13 The president of a university is concerned that illicit drug use on campus is higher than the 5% targeted level. A random sample of 250 students from a population of 2,000 revealed that 7 of them had used illicit drugs during the last 12 months. -Referring to Scenario 8-13, what is the upper bound of the 90% one-sided confidence interval for the proportion of students who had used illicit drugs during the last 12 months?

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 90% of the production lines and Design B for the remaining production lines, what is the risk of your investment?

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-group variation or SSA is __________.

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 70% of the production lines and Design B for the remaining production lines, what is the risk of your investment?

Twelve students in a Business Statistics class are to be formed into three teams of four. How many different ways can this be done?

SCENARIO 11-13 An important factor in selecting database software is the time required for a user to learn how to use the system. To evaluate three potential brands (A, B and C) of database software, a company designed a test involving five different employees. To reduce variability due to differences among employees, each of the five employees is trained on each of the three different brands. The amount of time (in hours) needed to learn each of the three different brands is given below: Software Operator A B C 1 17 17 23 2 18 17 23 3 14 13 19 4 12 11 18 5 19 17 22 Mean 16 15 21 $\text { Below is the Excel output for the randomized block design: }$ Source of Variation SS df MS F P-value Fcrit Rows 84.66667 4 21.16667 50.8 9.98-06 3.837853 Columns 103.3333 2 51.66667 124 9.54-07 4.45897 Error 3.333333 8 0.416667 Total 191.3333 14 -Referring to Scenario 11-13, the decision made at a 0.05 level of significance on the F test for the block effects implies that the blocking has been advantageous in reducing the experiment error.

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 2011 that consisted of 60 bushels of wheat, 40 bushels of corn, 35 bushels of soybeans and 70 hundredweight of milk in 2011 using 2008 as the base year?

The more expensive commodities are overly influential in an unweighted aggregate price index.