Suppose four teams, numbered one through four, play a single-elimination tournament, consisting of three games. Two teams play each game and one of them wins; ties do not occur. The tournament bracket is as follows: teams one and another team play each other in the first game and the remaining two teams play each other in the second game; the winner of the first game plays the winner of the second game in the third game.

Define a set ΩΩ so the elements of ΩΩ correspond to the possible outcomes of the tournament. An element of ΩΩspecifies the entire sequence of outcomes of the games. How many outcomes are there for the combination of what bracket is used and the game outcomes? (Assume the order the two games are played in the first round does not matter. For example, they could be simultaneous.)

A (time-homogeneous) Markov chain built on states A and B is depicted in the diagram below. What is the probability that a process beginning on A will be on B after 2 moves?

consider the Markov chain shown in Figure 11.14.

Figure 11.14- A state transition diagram.

1. Is this chain irreducible?
2. Is this chain aperiodic?
3. Find the stationary distribution for this chain.
4. Is the stationary distribution a limiting distribution for the chain?

To test Upper H 0​: mu equals 50 versus Upper H 1​: mu less than 50​, a random sample of size n equals 22 is obtained from a population that is known to be normally distributed. Complete parts​ (a) through​ (d) below. LOADING... Click here to view the​ t-Distribution Area in Right Tail. ​(a) If x over bar equals 47.1 and s equals 12.9​, compute the test statistic. t 0 equals nothing ​(Round to three decimal places as​ needed.)

1. Jace collected the following data on the quarterly room occupancy (in hundreds) for a resort hotel in Iowa.

1. Plot the data and describe any trend and seasonal effects you observe in the data.

2. Compute and interpret the seasonal indices.

3. Jace’s manager, Joseph, wants Jace to forecast the occupancy for four quarters of 2018. Can you help him (Forecast he room occupancy for four quarters of 2018)?

A medical investigation claims that the average number of infections per week at a hospital in Pennsylvania is at least 19.1. A random sample of 40 weeks had a mean number of 17.7 infections, and a sample standard deviation is 3.8. Is there enough evidence to reject the investigator’s claim? Use a 8 % level of significance to test this claim.

Consider the following hypothesis test:

H ₀:   50

H _a:  > 50

A sample of 60 is used and the population standard deviation is 7. Use the critical value approach to state your conclusion for each of the following sample results. Use  = .05.

a. With  = 52.5, what is the value of the test statistic (to 2 decimals)?
  

Can it be concluded that the population mean is greater than 50?
SelectYesNoItem 2

b. With  = 51, what is the value of the test statistic (to 2 decimals)?
  

Can it be concluded that the population mean is greater than 50?
SelectYesNoItem 4

c. With  = 51.8, what is the value of the test statistic (to 2 decimals)?
  

Can it be concluded that the population mean is greater than 50?
SelectYesNoItem 6

A customer service phone line claims that the wait times before a call is answered by a service representative is less than 3.3 minutes. In a random sample of 62 calls, the average wait time before a representative answers is 3.26 minutes. The population standard deviation is assumed to be 0.14 minutes. Can the claim be supported at α=0.08?

No, since test statistic is not in the rejection region defined by the critical value, reject the null. The claim is the alternative, so the claim is not supported

Yes, since test statistic is not in the rejection region defined by the critical value, reject the null. The claim is the alternative, so the claim is supported

Yes, since test statistic is in the rejection region defined by the critical value, reject the null. The claim is the alternative, so the claim is supported

No, since test statistic is in the rejection region defined by the critical value, reject the null. The claim is the alternative, so the claim is not supported

A study reported in the Journal of the American Medical Association investigated the cardiac demands of heavy snow shoveling. Ten healthy men underwent exercise testing with a treadmill and a cycle ergometer modified for arm cranking. The men then cleared two tracts of heavy, wet snow by using a lightweight plastic snow shovel and an electric snow thrower. Each subject's heart rate during snow removal were compared with the values obtained during treadmill and arm-crank ergometer testing. Dataset: HeartRate

a) Which technique of analyzing data should be used here? Why? Explain

b) Prepare the proper ANOVA table

c) Run the appropriate test statistics for this technique. Set up the hypothesis for your appropriate tests and conclude in the context of this problem. (hypotheses, decision rule, decision, conclusion in the context)

when estimating a population parameter from a simple random sample, the accuracy of the estimate depends primarily on

whatistheinteriorpointpenaltyfunctionmethod?Whatistheexteriorpoint
penaltyfunctionmethod?

In Star Trek, the original series, Captain Kirk was often depicted ignoring the prime directive of non-interference in other cultures. To determine if the crew approved of this 25 crew members were asked and 10 approved of the captain's methods. Find a 99% confidence interval for the true proportion of crew members who approve of Captain Kirk.

Do US adults consume an average of more than 75 grams of fat per day? According to a study of 600 adults in a scientifically designed study, the sample mean was 77.23 grams with sample standard deviation 33.47 grams. Do all the steps of a hypothesis test using normal theory methods, including finding the p-value, and write the conclusion in context.

In Star Wars Episode 4: A New Hope, Princess Leia says Luke is "a little short to be a storm trooper." To test this we went to New Orleans Comic-Con and took the heights, in inches, of Luke cosplayers and Storm Trooper cosplayers, the data is in the table below.

Use this data, the assumption that the population variances are equal, give a 95% confidence interval for μ S − μ L. Can you conclude that Luke was too short to be a storm trooper?

Group of answer choices

a)None of these

b)3±1.96910+415, The interval does not include 0 so Luke was too short

c)3±1.965.96(910+415), The interval includes 0 so Luke may not have been too short

d)3±2.0695.96(110+115), The interval does not include 0 so Luke was too short

e)3±2.0605.96(110+115), The interval does not include 0 so Luke was too short

Assume that adults were randomly selected for a poll. They were asked if they​ "favor or oppose using federal tax dollars to fund medical research using stem cells obtained from human​ embryos." Of those​ polled,

484484

were in​ favor,

395395

were​ opposed, and

118118

were unsure. A politician claims that people​ don't really understand the stem cell issue and their responses to such questions are random responses equivalent to a coin toss. Exclude the

118118

subjects who said that they were​ unsure, and use a

0.010.01

significance level to test the claim that the proportion of subjects who respond in favor is equal to

0.50.5.

What does the result suggest about the​ politician's claim?