A new vaccination is being used in a laboratory experiment to investigate whether it is effective. There are 246246 subjects in the study. Is there sufficient evidence to determine if vaccination and disease status are related?

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A new vaccination is being used in a laboratory experiment to investigate whether it is effective. There are 246246 subjects in the study. Is there sufficient evidence to determine if vaccination and disease status are related?

A. State the null and alternate hypothesis.
B. Find the expected value for the number of subjects who are vaccinated and are diseased.
C. Find the expected value for the number of subjects who are not vaccinated and are not diseased.
D. Find the value of the test statistic.
E. Find the critical value of the test at the 0.01 level of significance.
F. Make the decision to reject or fail to reject the null hypothesis at the 0.01 level of significance.
G. State the conclusion of the hypothesis test at the 0.01 level of significance.

4. Consider the random variable Z from problem 1, and the random variable X from problem 2.

Also let f(X,Z)represent the joint probability distribution of X and Z.  f is defined as follows:

f(1,-2) = 1/6
f(2,-2) = 2/15
f(3,-2) = 0
f(4,-2) = 0
f(5,-2) = 0
f(6,-2) = 0
f(1,3) = 0
f(2,3) = 1/30
f(3,3) = 1/6
f(4,3) = 0
f(5,3) = 0
f(6,3) = 0
f(1,5) = 0
f(2,5) = 0
f(3,5) = 0
f(4,5) = 1/6
f(5,5) = 1/6
f(6,5) = 1/6

Compute the covariance of X and Z.

Then, compute the correlation coefficient of X and Z. (Note: You will need values that you computed in problems 1 and 2.)

These are questions 1 and 2.

1. Let Z be a random variable with the following probability distribution f:

f(-2) = 0.3
f(3) = 0.2
f(5) = 0.5

Compute the E(Z), Var(Z) and the standard deviation of Z.

2. Tossing a fair die is an experiment that can result in any integer number from 1 to 6 with equal probabilities. Let X be the number of dots on the top face of a die. Compute E(X) and Var(X).

In an? experiment, 32 ?% of lab mice cells exposed to chemically produced cat Mups responded positively? (i.e., recognized the danger of the lurking? predator). Consider a sample of 200 lab mice? cells, each exposed to chemically produced cat Mups. Let x represent the number of cells that respond positively. Complete parts a through d below.

a. Explain why the probability distribution of x can be approximated by the binomial distribution.

There are

nothing

identical trials. For each? trial, there

?

are two

are many

is one

possible? outcome(s). The probability of each possible outcome

?

is different

is the same

for each? trial, and the trials are all

?

independent.

related.

b. Find? E(x) and interpret its? value, practically.

?E(x)equals

nothing

?(Round to the nearest whole number as? needed.)

Interpret this value. Choose the correct answer below.

A.

Exactly? E(x) cells out of

200

will respond positively in similar experiments.

B.

On average? E(x) cells out of

200

will respond positively in similar experiments.

C.

At most? E(x) cells out of

200

will respond positively in similar experiments.

D.

At least? E(x) cells out of

200

will respond positively in similar experiments.

c. Find the variance of x.

The variance of x is

nothing

.

?(Round to two decimal places as? needed.)

d. Give an interval that is? 95% likely to contain the value of x.

Using the empirical? rule, x is likely in the interval

?(nothing

?,nothing

?).

?(Round to one decimal place as? needed.)

Micromedia offers computer training seminars on a variety of topics. In the seminars each student works at a personal computer, practicing the particular activity that the instructor is presenting. Micromedia is currently planning a two-day seminar on the use of Microsoft Excel in statistical analysis. The projected fee for the seminar is $600 per student. The cost for the conference room, instructor compensation, lab assistants, and promotion is $9600. Micromedia rents computers for its seminars at a cost of $60 per computer per day, which must be reserved and paid for before the seminar. There is no refund for unused computers. The demand for the seminar varies as follows:

Demand    Probability
10    0.15
20    0.40
30    0.30
40    0.10
50    0.05

Build a simulation model to find out what would be a good number of computers reserved now. Then run it 10,000 times (with 2-way data-table with "computers to reserve now" as the row input). Note that Micromedia cannot admit students any more if they run out of the reserved computers. That is, if there are more students who like to attend the seminar than the number of computers reserved, the excess students cannot attend the seminar.

Question 1 (2 points)

If they reserve 15 computers now, the average profit is

Your Answer:

Question 2 (2 points)

If they reserve 30 computers now, the average profit is

Your Answer:

Question 3 (2 points)

If they reserve 45 computers now, the average profit is

Your Answer:

Question 4 (2 points)

If they reserve 35 computers now, the probability that the profit is positive is

Your Answer:

What is the income distribution of super shoppers? A supermarket super shopper is defined as a shopper for whom at least 70% of the items purchased were on sale or purchased with a coupon. In the following table, income units are in thousands of dollars, and each interval goes up to but does not include the given high value. The midpoints are given to the nearest thousand dollars.

(a)

Using the income midpoints x and the percent of super shoppers, do we have a valid probability distribution? Explain.

Yes. The events are distinct and the probabilities do not sum to 1. Yes. The events are indistinct and the probabilities sum to less than 1.     Yes. The events are distinct and the probabilities sum to 1. No. The events are indistinct and the probabilities sum to more than 1. No. The events are indistinct and the probabilities sum to 1.

(b)

Use a histogram to graph the probability distribution of part (a). (Select the correct graph.)

(c)

Compute the expected income μ of a super shopper (in thousands of dollars). (Enter a number. Round your answer to two decimal places.)
μ = thousands of dollars

(d)

Compute the standard deviation σ for the income of super shoppers (in thousands of dollars). (Enter a number. Round your answer to two decimal places.)
σ = thousands of dollars

The Europa Company has a large warehouse in Florida to store its inventory of goods until they are needed by the company’s many furniture stores in that area. A single crew with four members is used to unload and/or load each truck that arrives at the loading dock of the warehouse. Management currently is downsizing to cut costs, so a decision needs to be made about the future size of this crew.

Trucks arrive randomly at the loading dock at a mean rate of 2 per hour. The time required by a crew to unload and/or load a truck has an exponential distribution with a mean given by (60/n) minutes where n is crew size. The cost of providing each member of the crew is $20 per hour. The cost that is attributable to having a truck not in use (i.e., a truck standing at the loading dock) is estimated to be $30 per hour.

1. For the crew-size you determine in (b), calculate the following:

1. Average utilization of crew
2. Average number of trucks waiting to be unloaded
3. Average time in queue
4. Probablity at least 2 trucks will be waiting to be unloaded
5. Probability a truck will have to wait at least 1 hour prior to unloading
6. Probability that a truck will be in and out of the dock in 1 hour

2. Using the same crew-size as in (a), assume that with the use of modern lifting equipment, the standard deviation of unloading time is reduced by 50%. This means service time no longer has an exponential distribution. Calculate:
   1. The average number of trucks waiting to be unloaded
   2. The average time in queue
   3. Compare your answers with those for part (c). What is the explanation for the difference?

a. About % of the area under the curve of the standard normal distribution is outside the interval z=[−0.3,0.3]z=[-0.3,0.3] (or beyond 0.3 standard deviations of the mean).

b. Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1.

If P(−b<z<b)=0.6404P(-b<z<b)=0.6404, find b.

b=

c. Suppose your manager indicates that for a normally distributed data set you are analyzing, your company wants data points between z=−1.6z=-1.6 and z=1.6z=1.6 standard deviations of the mean (or within 1.6 standard deviations of the mean). What percent of the data points will fall in that range?

Answer:  percent (Enter a number between 0 and 100, not 0 and 1 and round to 2 decimal places)

d. A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.6 years, and standard deviation of 3.1 years.

If you randomly purchase one item, what is the probability it will last longer than 20 years?

e. A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 224-cm and a standard deviation of 1.8-cm. For shipment, 27 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is between 223.6-cm and 224.2-cm.
P(223.6-cm < M < 224.2-cm) =

Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 4.5 years and a standard deviation of 0.6 years. He then randomly selects records on 29 laptops sold in the past and finds that the mean replacement time is 4.2 years.

Assuming that the laptop replacement times have a mean of 4.5 years and a standard deviation of 0.6 years, find the probability that 29 randomly selected laptops will have a mean replacement time of 4.2 years or less.
P(M < 4.2 years) =  
Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.945 g and a standard deviation of 0.314 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 43 cigarettes with a mean nicotine amount of 0.864 g.

Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly seleting 43 cigarettes with a mean of 0.864 g or less.
P(M < 0.864 g) =  
Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

write a program in matlab to produce a discrete event simulation of a switching element with 10 inputs and 3 outputs. Time is slotted on all inputs and outputs. Each input packet follows a Bernoulli process. In a given slot, the independent probability that a packet arrives in a slot is p and the probability that a slot is empty is (1– p). One packet fills one slot. For a switching element if 3 or less packets arrives to some inputs, they are forwarded to the switching element outputs without a loss. If more than 3 packets arrive to the inputs of the switching element, only 3 packets are randomly chosen to be forwarded to the switching element outputs and the remaining ones are discarded. In your simulation the program will mimic the operation of the switch and collect statistics. That is, in each time slot the program randomly generates packets for all inputs of the switching element and counts how many packets can be passed to the output of the switching element (causing throughput) and, alternatively counts how many packets are dropped (when the switching element has more than 3 input packets at a given time slot) . Your task is to collect throughput statistics for different values of p (p = 0.05, 0.1 up to 1.0 in steps of 0.05), by running the procedure described above for each value of p and for many slots (at least a thousand slots per value of p). The more simulated slots, the more accurate the results will be. Based on this statistics, plot two graphs: 1) the average number of busy outputs versus p, and 2) the average number of dropped packets versus p.