Exam 20: Probability and Combinatorics

The Laspeyres price index has the disadvantage that the consumption pattern in the initial period might be quite different from that in the current period and, hence, does not reflect accurately the current consumption cost.

SCENARIO 12-19 The director of transportation of a large company is interested in the usage of the company's van pool program. She surveyed 129 of her employees on the usage of the program before and after a campaign to convince her employees to use the service and obtained the following: She will use this information to perform test using a level of significance of 0.05. -Referring to Scenario 12-19, the director now wants to know if the proportion of employees who use the service before the campaign and the proportion of employees who use the service after the campaign are the same. What is the p-value of the test statistic using a 5% level of significance?

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 null hypothesis for the randomized block F test for the difference in the means should be rejected at a 0.05 level of significance.

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 value of the test statistic for the randomized block F test for the difference in the means?

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, the confidence interval estimate of the mean with finite population correction will be wider in range than confidence interval estimate without finite population correction.

SCENARIO 5-11 There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: -Referring to Scenario 5-11, what is the total variance of value gain if you invest in both houses?

To construct a bootstrap confidence interval estimate for the population mean, you will resample the initial sample by selecting n values with replacement from the n values in the initial sample for m different times.

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 Studentized range distribution for the Tukey multiple comparison procedure?

The Human Resources Director of a large corporation wishes to develop an employee benefits package and decides to select 500 employees from a list of all (N = 40,000) workers in order to study their preferences for the various components of a potential package. In this study, methods that result in decisions concerning population characteristics based only on the sample results are called _______.

The O in the DCOVA framework stands for "operationalize".

A company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of waiting Time was found to be a variable best approximated by an exponential distribution with a mean Length of waiting time equal to 2.8 minutes (i.e. the mean number of calls answered in a minute is 1/2)8). What is the probability that a randomly selected caller is placed on hold fewer than 7 Minutes?

The Laspeyres price index is a form of weighted aggregate price index.

The bootstrap confidence interval estimate for the population mean is constructed based on the sampling distribution of the m resampled means.

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 are the degrees of freedom of the randomized block F test for the difference in the means at a level of significance of 0.01?

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 expected profit?

SCENARIO 16-16 Given below are the average prices for three types of energy products for five consecutive years. Year Electricity Natural Gas Fuel Oil 1 43.205 25.893 0.892 2 16.959 28.749 0.969 3 47.202 28.933 1.034 4 48.874 29.872 0.913 5 48.693 28.384 0.983 -Referring to Scenario 16-16, what are the simple price indices for electricity, natural gas and fuel oil, respectively, in year 4 using year 1 as the base year?

SCENARIO 9-15 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 9-15, 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 marketing the new local anesthetic when its population mean effective time is greater than the 7.4 minutes is _____ if the population mean effective time is 8 minutes.

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 null hypothesis for the randomized block F test for the difference in the means is a) $H _ { 0 } : \mu _ { A } = \mu _ { B } = \mu _ { C } = \mu _ { D }$ b) $H _ { 0 } : \mu _ { K _ { y l e } } = \mu _ { \text {Sarah } } = \mu _ { \text {Leigh } } = \mu _ { \text {Issac } }$ c) $H _ { 0 } : M _ { A } = M _ { B } = M _ { C } = M _ { D }$ d) $H _ { 0 } : M _ { K y l e } = M _ { \text {Sarah } } = M _ { \text {Leigh } } = M _ { \text {Issac } }$

To construct a bootstrap confidence interval estimate for the population mean, you typically select a very large number (in the thousands) of resamples.

There are 47 contestants at a national dog show. How many different ways can contestants fill the first place, second place, and third place positions?