Test the given claim. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, and then state the conclusion about the null​ hypothesis, as well as the final conclusion that addresses the original claim. Among 2010 passenger cars in a particular​ region, 226 had only rear license plates. Among 394 commercial​ trucks, 58 had only rear license plates. A reasonable hypothesis is that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. Use a 0.01 significance level to test that hypothesis.

a. Test the claim using a hypothesis test.

b. Test the claim by constructing an appropriate confidence interval.

Which method (statistic) do you use for detecting the violation of the assumption for the repeated-measures ANOVA? What is the assumption for the repeated-measures ANOVA?

Explain what is meant by the following time series terms

i) Sample autocorrelation function

ii) The if and only if conditions for the stationarity of the ARMA(p,q) process

iii) The partial autocorrelation function

The company manufactures chocolate bars with nominal weight of 115 g per bar. In order to to avoid risk of short changing, the mean weight is set as 117 g and SD of 2 g.

What is the probability that :

(a) a random chocolate bar weighs between 116 gram and 120 gram?

(b) a particular sample mean would be less than 116.5 millimeters chosen of 40 random samples of chocolate bar.

Random samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and Population 2 does not. The data from these two samples is given below:

Population 1: 71, 63, 68, 71, 72, 66, 73

Population 2: 68, 78, 71, 68, 75, 69, 76, 72

Is there evidence, at an α=0.07 level of significance, to conclude that there those who exercise regularly have lower resting heart rates? Carry out an appropriate hypothesis test, filling in the information requested.

A. The value of the standardized test statistic:

Note: For the next part, your answer should use interval notation. An answer of the form (−∞,a)(−∞,a) is expressed (-infty, a), an answer of the form (b,∞)(b,∞) is expressed (b, infty), and an answer of the form (−∞,a)∪(b,∞)(−∞,a)∪(b,∞) is expressed (-infty, a)U(b, infty).

B. The rejection region for the standardized test statistic:

C. The p-value is

D. Your decision for the hypothesis test:

A. Reject H0
B. Do Not Reject H1
C. Do Not Reject H0
D. Reject H1

You draw 40 times with replacement from a bag containing 7 red marbles and 3 blue marbles.

A) What is the chance you will get exactly 8 blue marbles? Explain if you should use binomial formula or normal approximation.

B) What is the chance that you get fewer than 20 blue marbles?Explain if you should use binomial formula or normal approximation.

INDEPENDENT SAMPLES T-TEST #1

When people think about legendary basketball franchises, they often think about the New York Knicks. (Well, kind of.) When people think about terrible basketball teams, they often think about the Sacramento Kings. Guess what? When you look at their recent history, neither team has been particularly great. Here are the number of games that each team has won during the last five seasons.

Sacramento New York

2014-2015 29 17

2015-2016 33 32

2016-2017 32 31

2017-2018 27 29

2018-2019 39 17

Based on those six seasons, is there a significant difference between the Kings and the Knicks in terms of how many games they won per season?

Here are the formulas: df =

Do an independent-samples t-test. (NOTE: You may use Excel or Google to get the standard deviations, but remember that the variance requires you to square the standard deviation.) Make sure you include the following in your answer:

A) What is the null hypothesis? What is the alternative hypothesis? (0.5 points)

B) Show all work for how you got your t-statistic. I will allow you to use Excel or Google to calculate the means and variances! Please do not make your life harder than it has to be! The numbers will get large, but you can round liberally. (3.5 points)

C) What is your critical value (and why), and explain to me why you kept or rejected the null. (1 point)

If you can explain your reasoning that will be appreciated.

You have been trapped in a building with 3 hallways, and each of them can lead to freedom.

Unfortunately for you, each of these 3 hallways has 2 doors. Each of the six doors could be

locked or unlocked independent of any other door. To be able to escape to

freedom through a particular hallway, you require that both the doors in that hallway are

unlocked.

The doors in hallway 1 is independently locked with probability 1/2

The doors in hallway 2 is independently locked with probability 1/3

The doors in hallway 3 is independently locked with probability 1/4

What is the probability that hallway 1 was open (in essence, both doors in hallway A were

unlocked) given that you managed to escape to freedom? Assume that if a hallway is closed you can go back and try another one.

A psychologist wants to estimate the mean of IQ scores. It is widely believed that IQ scores follow a normal distribution. Her random sample of 20 IQ scores has a mean of 97 and a standard deviation of 17.6 . Find the 95% confidence interval for the population mean based on this sample. State the Best point estimate, Margin of Error and Include the written statement.

please list all the work.

Among all the possible permutations that can be made by all the characters from the series of words "COMPUTER", how many different ways that always and only three characters are in between 'P' and 'R''? Show both your work and the exact number.

In the 2016 Summer Olympics in Rio, there were eight runners in the final of the men's 100 meter dash. How many possible outcomes could we have seen on the podium?

(The podium honors the first three finishers in an ORDERED fashion. The first-place finishers gets the gold medal, second-place finisher gets the silver medal, and the third-place finisher gets the bronze medal.)

How many possible outcomes could we have seen on the podium that didn't include either of the two Americans? Remember the podium represents an ORDERED finish.

What is the probability that both of the American runners medalled? (To medal means to finish in the top three)

**Calculate under the assumption that order doesn't matter for this calculation.

How many possible outcomes could we have seen on the podium if we know that a runner from Jamaica finished first, a runner from America finished second, and a runner from neither Jamaica nor America finished third?

Has the consumption of red meat decreased over the last 10 years? A researcher selected hospital nutrition records for 400 subjects surveyed 10 years ago and compared the average amount of beef consumed per year to amounts consumed by an equal number of subjects interviewed this year. The data are given in the table.
Ten Years Ago This Year
Sample Mean 71 64
Sample Standard Deviation 20 26

(a) Find the test statistic and the p-value. (Round your test statistic to two decimal places and your p-value to four decimal places.)

z =

p-value =

(b) Find a 99% lower confidence bound for the difference (ten years ago − this year) in the average per-capita beef consumptions for the two groups. (Round your answer to two decimal places.)

One state lottery game has contestants select 5 different numbers from 1 to 45. The prize if all numbers are matched is 2 million dollars.  The tickets are $2 each.

Please show work.

1)    How many different ticket possibilities are there? Hint: use combinations here 45 C 5.  Order of the numbers doesn't matter, just matching them, so we don't need permutations.  

2)    If a person purchases one ticket, what is the probability of winning? What is the probability of losing?

3)    Occasionally, you will hear of a group of people going in together to purchase a large amount of tickets. Suppose a group of 30 purchases 6,000 tickets.

a)    How much would each person have to contribute?

b)    What is the probability of the group winning? Losing?

4)    How much would it cost to “buy the lottery”, that is, buy a ticket to cover every possibility? Is it worth it?

5)    Create a probability distribution table for the random variable x = the amount won/lost when purchasing one ticket.

6)    In fair games, the expected value will be $0. This means that if the game is played many…many times, then one is expected to break even eventually. This is never true for Casino and Lottery games.   Find the expected value of x = the amount won/lost when purchasing one ticket.

7)    Interpret the expected value.  

8)    Fill in the following table using the expected value.