Timothy quits his job which pays $86000 a year , to enroll in a 3 year graduate program. His annual school expenses are $64900 for tuition, $8500 for books, and $1300 for food.

1. What is his opportunity cost for attending the graduate program?

A motor vehicle assembly plant requires the use of both capital and labour. The Tesla manufacturing plant is considering increasing the numbers of workers to production.

1. Does Diminishing Return hold in this scenario? (YES/NO)

2. Explain answer

The researcher conducted a hypothesis test and found the 95% confidence interval to examine whether there is a difference in high school students completion rate in percent with respect to the size of the teachers' salary (low or medium). The hypothesis test result showed p-value of 0.59 and the CI was [-2.45, 4.45].

In the space provided below,

a) Explain whether the hypothesis test result and the confidence interval are in agreement.

b) Explain whether and why Type 1 error or Type 2 error could occur in this study.

Please show answer using R commands.

Exercise 3: Bob is a high school basketball player. He is a 60% free throw shooter. That means his probability of making a free throw is 0.60. Use R commands to answer the following questions. (

(a) During the season, what is the probability that Bob makes his third free throw on his sixth shot? 

(b) What is the probability that Bob makes his first free throw on his sixth shot?

Amelia wants to estimate what proportion of her community members favor a tax increase for more local
school funding. She wants her margin of error to be no more than 2% at the 95% condence level. What is
the smallest sample size required to obtain the desired margin of error?

(2) Suppose a preliminary poll reveals that 45% of 50 voters support a presidential candidate. At 95% condence,
how large a sample is needed to obtain a margin of error of 4 percentage points?

Recently a researcher reported a correlation of -.57 across 30 high schools in the state between mean teacher salary and the per student vandalism rate of the school (these are not actual data and should be used only for purposes of this take-home). Interpret this finding. What do you believe is the most likely reason that these two variables correlate? (Be specific: if, for example, you believe that there is a third, fourth, etc., variable operating here, please indicate what variable it is and how it may affect the correlation.)

Suppose you are interested in measuring the amount of time, on average, it takes you to make your commute to school. You've estimated that the average time is 35.68 minutes with a standard deviation of 6.17 minutes. Assuming that your estimated parameters are correct and the commute time is normally distributed, what is the probability that the average commute time of 11 random days is greater than 36.86 minutes? Question 8 options: 1) 0.2629 2) 0.7371 3) 0.5758 4) 0.8246 5) 0.4242

List the type of correlation and casual relationship that you would expect to find for each of the following pairs of variables. a) the price of gasoline at the pump, the current world price of crude oil b) the fish population in a lake, the number of cottages around the lake c) the humidex rating (an index based on air temperature and humidity), the number of respiratory ailments reported d) the stock price of a telephone company, the cost of car insurance e) parents’ educational level, their children’s success in school?

While direct sunlight is unpolarized, light coming from a clear blue sky is linearly polarized to some extent. Assume all the light from the blue sky is linearly polarized in the same direction. Suppose a school library has installed skylight windows in the ceiling of the atrium to allow for natural lighting. The windows are polarized so that the intensity of light from the polarized blue sky is reduced by 58%. What is the angle between the polarization direction of the light and the polarization axis of the windows? __________°

The economy is experiencing a short-run recession (low levels of output and high rates of unemployment). You are the chief economic advisor of the federal government. In each of the following two cases, propose a concrete example of policy that the government can implement to boost the economy. Be specific on how each policy would affect output, unemployment, and price level using the AD-AS model.

1. Assume that you are from the Keynesian (mainstream) school of thought.

2. Assume that you adhere to the real business cycle view

Listed below are alumnus’s contribution (in dollars) and the years the alumnus has been out
of school for a small college.

a) Find the value of the linear correlation coefficient r and use a significance level of α = 0.05 to
determine whether there is a significant linear correlation between the two variables.

b) Find the best predicted value for the contribution of an alumnus after 4 years.