For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a random sample of 520 judges, it was found that 291 were introverts.

(a) Let p represent the proportion of all judges who are introverts. Find a point estimate for p. (Round your answer to four decimal places.)


(b) Find a 99% confidence interval for p. (Round your answers to two decimal places.)

Give a brief interpretation of the meaning of the confidence interval you have found.

We are 99% confident that the true proportion of judges who are introverts falls outside this interval.We are 1% confident that the true proportion of judges who are introverts falls above this interval.    We are 99% confident that the true proportion of judges who are introverts falls within this interval.We are 1% confident that the true proportion of judges who are introverts falls within this interval.

(c) Do you think the conditions np > 5 and nq > 5 are satisfied in this problem? Explain why this would be an important consideration.

Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.    No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a random sample of 63 professional actors, it was found that 39 were extroverts.

(a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.)


(b) Find a 95% confidence interval for p. (Round your answers to two decimal places.)

Give a brief interpretation of the meaning of the confidence interval you have found.

We are 5% confident that the true proportion of actors who are extroverts falls within this interval.We are 95% confident that the true proportion of actors who are extroverts falls outside this interval.    We are 5% confident that the true proportion of actors who are extroverts falls above this interval.We are 95% confident that the true proportion of actors who are extroverts falls within this interval.

(c) Do you think the conditions np > 5 and nq > 5 are satisfied in this problem? Explain why this would be an important consideration.

Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.    Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.

Assume that the mean SAT score of students admitted to Northeastern Illinois University is 1090. The members of the Psychology Department believe that students who decide to major in Psychology have higherSAT scores than the general population of students at the university. A sample of N= 10 newly declared Psychology majors consent to have their entrance records reviewed.

Their scores are as follows: 1276, 1248, 1066, 1106, 1138, 1215, 1168, 1185, 933, and 1425.Can the department conclude that Psychology majors have higher SAT scores than the university as a whole?

(a)Set up your hypotheses using the correct notation (1mark)

(b)Compute tobt(1.5marks)

(c)What is the statistical decision? JUSTIFY YOUR ANSWER (1mark)

(d)What is the conclusion? (1mark)

(e)Compute the 95% Confidence Interval for μ (1 mark)

Suppose the wheat growing industry in the US is perfectly competitive and there is free entry in the long run. the market demand function is Qd= 580 -4p, which is measured in tons per month. each producer in the industry has a fixed cost of $400 and a variable cost function given by VC=q^2 +5q, where q is the output of an individual producer.

a)calculate the long run market equilibrium price and quantity. How many firms are there in the economy?

Suppose the marginal cost increases by 2$ from the long run equilibrium. At the same time the market demand decreases by 34. Answer the following:

b) calculate the new short run market equilibrium price and quantity

c) what is the profit of each individual firm in the short run?

d) Draw a graph to show the short run and long run response of the economy. Mark the short run and long run equilibrium price and quantity on the graph.

the US has removed its prior ban on exporting crude oil. what has been the impact of the new policy? what is your position on this issue? who wins? who loses?

The computer center at Rockbottom University has been experiencing computer downtime. Let us assume that the trials of an associated Markov process are defined as one-hour periods and that the probability of the system being in a running state or a down state is based on the state of the system in the previous period. Historical data show the following transition probabilities: To From Running Down Running 0.70 0.30 Down 0.20 0.80 If the system is initially running, what is the probability of the system being down in the next hour of operation? If required, round your answers to two decimal places. The probability of the system is What are the steady-state probabilities of the system being in the running state and in the down state? If required, round your answers to two decimal places. = =

Key figures for Apple and Google follow.

Required:
1. Compute times interest earned for the three years' data shown for each company.
2. In the current year, and using times interest earned, which company appears better able to pay interest obligations?
3. In the current year, and using times interest earned, is the company in a good or bad position to pay interest obligations for (a) Apple, and (b) Google? Assume an industry average of 10.

Compute times interest earned for each of the three years shown. (Round your answer to 2 decimal places.)

why would a scientist who needs to know the population size of an organism not simply count every individual of a species in an area?

With regard to preserving and protecting the environment, who has the most important role to play - government, individual consumers, or businesses and why?

A 59 year-old calendar year individual taxpayer purchased an annuity from an insurance company for $100,000 in 2019. The terms of the annuity were that the company would pay him $5,000 a year to T for the rest of T’s life. How much income will he include in his personal income tax return as a result of receiving the $5,000 payment

in 2020?   _____________

In 2050? ______________