Exam 20: Probability and Combinatorics

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, what is the total variance of the profit if you increase the shift of your production lines and choose to produce both designs?

To construct a bootstrap confidence interval estimate for the population mean, you will resample the initial sample of size n by selecting n values without replacement from the n values in the initial sample for m different times.

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 F test for the block effects should be rejected at a 0.05 level of significance.

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, using the 90% one-sided confidence interval, the president can be 85% confident that no more than 5% of the students at the university had used illicit drugs during the last 12 months.

The interval between patients arriving at an outpatient clinic follows an exponential distribution with mean 15 minutes. What is the mean number of arrivals per minute?

To test whether one proportion is higher than the other in two related samples, you can use the Marascuilo procedure.

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes Over $50,000 and 70% had 2 cars. The probability that annual household income is over $50,000 If the residents of a household do not own 2 cars is:

An exploration team of 2 women and 3 men is to be chosen from a candidate pool of 6 women and 7 men. How many different ways can this team of 5 be formed?

To determine the probability of getting at least 3 events of interest in a binomial distribution, you will find the area under the normal curve for X = 2.5 and above.

The estimation of the population average family expenditure on food based on the sample average expenditure of 1,000 families is an example of

The number of males selected in a sample of 5 students taken without replacement from a class of 9 females and 18 males has a hypergeometric distribution.

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 decision made at a 0.05 level of significance on the randomized block F test for the difference in means implies that all 4 means are significantly different.

The McNemar test is approximately distributed as a Student's t.

"Big data" are data being collected in huge volumes and at very fast rates, and they typically arrive in a variety of forms, organized and unorganized.

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 is not from out-of-state, the probability the student has passed the ELM is ________.

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 not include any of the twin brothers?

An Undergraduate Study Committee of 6 members at a major university is to be formed from a pool of faculty of 18 men and 6 women. If the committee members are chosen randomly, what is the probability that all of the members will be men?

The interval between patients arriving at an outpatient clinic follows an exponential distribution at a rate of 1.5 patients per hour. What is the probability that a randomly chosen arrival to be between 10 and 15 minutes?

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, based on the Tukey multiple comparison procedure with an overall level of significance of 0.01, the agronomist would decide that there is a significant difference between the crop yield of Smith and Walsh seeds.

SCENARIO 9-11 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 9-11, if you select a sample of 20 compact microwave ovens and are willing to have a level of significance of 0.10, the probability of making a Type II error is _____ if the mean power consumption of all such microwave ovens is in fact 257.3 W.