Assignment #6

This is the last assignment of the course! I have decided against changing our usual schedule. As a result, this assignment will be due at the typical time, that is, 10 minutes before class time next Wednesday. In spite of the possibility that I had alluded to during lecture, there will not be any additional questions to follow. For students in section 401, you will not be able to answer the last question until after lecture on Monday (unless you choose to read ahead).

## Problem #1: (2/3/3)

You are cruising along Western avenue and note that you rarely hit red lights. In fact, you find out that under Mayor Rahm Emmanuel, the lights have been syncrhonized along busy thoroughfares so that they are red only 30% of the time. Your route takes you through 4 lights.

What is the likelihood that you will hit 0 red lights?

What is the likelihood that you will hit two or more red lights?

What about hitting all 4 red lights?

## Problem #2: (3/2/2/3)

In the language of government statistics, you are “in the labor force” if you are available for work and either working or actively seeking work. The unemployment rate is the proportion of the labor force (not of the entire population) who are unemployed. Here are data from the Current Population Survey for the civilian population aged 25 years and over. The table entries are counts in thousands of people:

 Highest Education Total Population In Labor Force Employed Did not finish HS 28,021 12,623 11,552 HS, but no college 59,844 38,210 36,249 Some college, but not bachelor’s degree 46,777 33,928 32,429 College Graduate 51,568 40,414 39,250

(a)    Find the unemployment rate for people with each level of education. How does the unemployment rate change with education? Explain carefully why your results show that level of education and being unemployed are not independent.

(b)   What is the probability that a randomly chosen person from the population in the previous question is unemployed?

(c)    What is the probability that a person is employed given that they have completed HS but have not attended college

(d)   Are the events ‘Did not finish High School’ and ‘College Graduate’ independent? Explain carefully.

## Problem #3: (4/4)

The total sleep time in a population of college students was approximately Normally distributed with a mean of 7.02 hours and standard deviation of 1.15 hours. Suppose you plan to take an SRS of size 200 and compute the average sleep time.

(a) What is the mean and standard deviation of your sample?

(b) What is the probability of coming up with a sample that shows that they slept 6.9 hours or less?

## Problem #4: (8)

You want to rent an unfurnished one-bedroom apartment in Boston next year. The mean monthly rent for a random sample of 10 apartments advertised in the local newspaper is \$980. Assume that the standard deviation is \$290. Find the 90%, 95%, and 99% confidence intervals for the mean monthly rent for this category of apartments.

Look at the 95% confidence interval and say whether this statement is true or false. Be sure to explain your answer:  This interval describes the price of 95% of the rents of all the unfurnished one-bedroom apartments in the Boston area.

## Problem #5: (6)

Define Ha and Ho and P value. I do NOT want a paraphrase from the notes or textbook. By all means, read/review/youtube/friend-tube, etc as needed. However, I would then ask you to really think, that is, mentally review, these concepts on your own for a while. Then attempt to define these three terms in your own words.