Question

2. You observe five random numbers: 2,2,3,4,4. The mean of this data is 3. What is the standard deviation?

  

3

0.5

2

1

3. For a random variable with the mean and standard deviation you found in Question 2 above, what is standard deviation of the sample average in repeated samples where n=5? (In other words, what is the standard error of the sample mean when n=5?). Hints: To calculate the standard error, use the formula given in equation 1.6 of Mastering Metrics. The square root of 5 is 2.25.

4/9

8/9

2/9

2

1

4.On a can of sardines it is written that the can contains 10 sardines. You open up 100 cans and find the average is 9.75 sardines with a standard deviation of 1. What is the test statistic in a test of the null hypothesis that the population average is 10? Can you reject the null at the 5% significance level?

-2.5; yes

-0.25; yes

-2.5; no

-.25; no

5.The table below contains the raw data from Professor Rietz’s six bike trips between the train station and the MLK library. In addition to the date of the trip and the duration, it also tells the starting location and the ending location. Time is in minutes, rounded to the nearest whole number. As you can infer, Prof. Rietz arrives at the train station at the start of the day, bikes to campus, works on campus, and then bikes back to the station at the end of the day.

Date	Starting Location	Ending Location	Duration (minutes)
10/2	Train	Library	8
10/2	Library	Train	8
10/9	Train	Library	9
10/9	Library	Train	7
10/16	Train	Library	10
10/16	Library	Train	6

The average duration of trips starting at the Train Station was ___ while the average duration of trips starting at the Library was ___

9; 7

10; 6

6; 10

7; 9

6.Consider a test of the null hypothesis that there is no difference between the average duration of trips that start at the Library and trips that start at the Train Station. Which of the following is the approximate value of the appropriate test statistic for such a test? (Hint: use the test statistic formula in the middle of page 45 of MM; for the standard error that appears in the denominator of the test statistic formula, use the separate-variance formula that appears in footnote 17.)

Date	Starting Location	Ending Location	Duration (minutes)
10/2	Train	Library	8
10/2	Library	Train	8
10/9	Train	Library	9
10/9	Library	Train	7
10/16	Train	Library	10
10/16	Library	Train	6

2.4

3.7

3.8

1.2

4.2

Answer 1

2:

Following table shows the calculations:

	X	(X-mean)^2
	2	1
	2	1
	3	0
	4	1
	4	1
Total	15	4

Last option is correct.

3:

The standard error of mean is

First option is correct.

4:

Correct option is -2.5; yes.