**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).

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?

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.

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?

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*.

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.