Problem 1 (20 points)

Recently, YouGov/Economist surveyed 1,515 New Yorkers to inquire about their attitudes towards the Trump Administration. Among other questions, the survey asked, “Would you say things in this country today are...” Below, you’ll find the responses:

a)   Fill in the blank: According to the table                      % of Democrats responded “Off on the wrong track.”

b)   Fill in the blank:                     % more Republicans responded “Not sure” than Democrats.

c)   The variable “Response” is: (Check all that apply)

 nominal

 ordinal

 continuous

 skewed

 discrete

d)  A colleague reviews the data and concludes most Americans believe that things in this

country are “off on the wrong track.” Do you agree with this conclusion and why? (Please write one or two sentences to support your answer.)

AGREE                       DISAGREE

Circle One

Why?

Problem 2 (18 points)

Using the data from YouGov/Economist you would like to provide an 87% confidence interval estimate of the proportion of New Yorkers that think that the country is “generally headed in the right direction.”

The table is replicated here for your convenience:

Put your estimate in the rectangle below. Be sure to show all of your work and provide your interval estimate in the form:

 < the parameter you that you are estimating <           .

Part 2

True or False? If YouGov/Economist had used a sample of 500 New Yorkers your interval

would have been narrower. (You do not need to do the calculation. This is a thought question.)

TRUE                       FALSE

Circle One

Why? (Provide a short answer)

Problem 3 (20 points)

In 2015, Walk Score, a Redfin Company, ranked Minneapolis as the most bikeable city in the

U.S. The commute time in Minneapolis is normally distributed with a mean of 20.1 minutes with a standard deviation of 3.6 minutes. It was found that 9.7% of commuters bike to work. If a

commuter is selected at random, what is the probability that s/he will have a commute time: (Write final answer on lines provided.)

a)  between 22.7 and 29.5 minutes? Probability =                      

b)   More than 17.8 minutes?  Probability =                      

c)  What is the commute time that corresponds to the 86th  percentile?                      

d)  You are particularly interested in the commutes of people living on the east side of

Minneapolis. You are told that their commute times are not normally distributed but

instead positively skewed with a mean of 25.4 and a standard deviation of 4.2 .  If you

drew a random sample of 225 commuters from east Minneapolis, the probability that the mean of that sample would be less than 24.8 minutes is                      

Problem 4 (12 points)

According to the New York City Department of Transportation, before bike lanes were

introduced in the city, the mean commute time was 38 minutes. In a random sample of 45 New Yorkers today, the mean commute time was 32 minutes with a standard deviation of 8.3

minutes. Does your study suggest that commute times are now shorter? Steps 2 and 3.

Step 2: State null and research hypotheses

Step 3: Select the sampling distribution and set critical region (use alpha = .01)

Suppose that you do a one-sample hypothesis test and you reject the null hypothesis. Which of the following could be true (check all answers that are possible).

 You made a Type 1 error

 You made a Type 2 error

 You made a Type 1 and Type 2 error at the same time

 You reached a correct conclusion

Problem 5 (18 points)

In the European Union (EU), 7.3 million people hold managerial positions in enterprises with 10 employees or more: 4.7 million men (64.38% of all managers) and 2.6 million women (35.62%). Although representing approximately half of all employed people in the EU, women continue to  be underrepresented amongst managers. You are interested in the situation of women in the workforce in the U.S. You draw a sample of 500 managers in the U.S. of which 190 are women. Is the representation of women in managerial positions significantly different in the U.S. than in  the E.U.?

Step 2: State null and research hypotheses

Step 3: Select the sampling distribution and set critical region

Step 4: Compute the test statistic

Step 5: Make a decision