Exam 20: Probability and Combinatorics

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, what is the value of the test statistic using a 1% level of significance?

SCENARIO 8-14 The president of a university is concerned that the percentage of students who have cheated on an exam is higher than the 1% acceptable level. A confidential random sample of 1,000 students from a population of 7,000 revealed that 6 of them said that they had cheated on an exam during the last semester. -Referring to Scenario 8-14, using the 90% one-sided confidence interval, the president can be 95% confident that no more than 1% of the students at the university had cheated on an exam during the last semester.

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, what are the degrees of freedom of the randomized block F test for the difference in the means at a level of significance of 0.05?

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 at least 25 computers that require repair on a given day using a normal approximation.

The A in the DCOVA framework stands for "apply".

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 value of MSA is __________, while MSBL is __________.

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

There are 10 finalists at a national dog show. How many different orders of finishing can there be for all the 10 finalists?

The amount of time between successive TV watching by first graders follows an exponential distribution with a mean of 10 hours. The probability that a given first grader spends between 10 and 15 hours between successive TV watching is ______.

A financial analyst is presented with information on the past records of 60 start-up companies and told that in fact only 3 of them have managed to become highly successful. He selected 3 Companies from this group as the candidates for success. To analyze his ability to spot the Companies that will eventually become highly successful, he will use what type of probability Distribution?

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 no more than four of the new employees will be from University A?

To construct $( 1 - \alpha )$ 100% for the popul a bootstrap confation mean, you will order idence intethe resamrval estimate with confidepled means for the nce level 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 ?100% as the lower limit and the value of that cuts off the largest ?100% as the upper limit.

SCENARIO 4-13 A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or chicken. Of 200 respondents selected, 75 were children and 125 were adults. 120 preferred hamburger and 80 preferred chicken. 55 of the children preferred hamburger. -Referring to Scenario 4-13, assume we know that a person prefers hamburger. The probability that this individual is a child is __________.

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 unweighted aggregate price index for the basket of four food items in 2012 using 2008 as the base year?

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, there is evidence of a significant difference in the mean amount of time needed to learn Brand A and Brand B at the 5% level of significance?

SCENARIO 12-21 A filling machine at a local soft drinks company is calibrated to fill the cans at a mean amount of 12 fluid ounces and a standard deviation of 0.5 ounces. The company wants to test whether the standard deviation of the amount filled by the machine is 0.5 ounces. A random sample of 15 cans filled by the machine reveals a standard deviation of 0.67 ounces. -Referring to Scenario 12-21, what is the value of the test statistic?

SCENARIO 8-16 A random sample of 100 stores from a large chain of 500 garden supply stores was selected to determine the mean number of lawnmowers sold at an end-of-season clearance sale. The sample results indicated a mean of 6 and a standard deviation of 2 lawnmowers sold. A 95% confidence interval (5.623 to 6.377) was established based on these results. -Referring to Scenario 8-16, there are 10 possible samples of 100 stores that can be selected out of the population of 1,000 stores.

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, which of the following is one of the properties required so that the binomial distribution can be used to compute the probability that no more than 2 computers will Require repair on a given day?

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, what is the 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, which of the following is one of the properties required so that the binomial distribution can be used to compute the probability that no more than 2 computers will Require repair on a given day?