This quiz asks questions about fundamental statistical concepts, including two types of hypothesis tests.

Question Description

The first, a hypothesis test involving a single mean, is exemplified by another question about sardines. (There are not many exciting examples that illustrate this type of test.). The second type of hypothesis test is much more interesting and it involves the difference between two means (we call this a “difference in means” test.). You have been calculating differences in means using the health survey data; in this quiz, you will carry out a difference-in-means test using data on bicycle trip duration.

*** Note: All the questions, except the last one, are answerable using pen and paper. Indeed, you will come away from this class with a much better understanding of the concepts if you try to work through them “by hand” rather than first going to the computer or calculator. Thus, in addition to answering the quiz, you are required to send to me your written answers. You may scan you answers and email to me a pdf or type up your answers in Word and email it to me. You must turn in individual, NOT group, writeups, and cases of clear copying will be considered cheating and given a final score of 0.

1. True or False. In statistics, the result that in large enough samples, the mean of a random variable
is normally distributed, regardless of how the random variable is distributed, is called the Central
Limit Theorem

2.You observe five random numbers: 2,2,3,4,4. The mean of this data is 3. What is the standard deviation? (This should be done with a pen and paper, and the formula on p. 36, note 16 of

(1,3,2,0.5)

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.

8/9 1 2 2/9 4/9

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; no

-2.5; yes

-.25; no

-.25; yes

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.

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

6; 10

10; 6

9; 7

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.)

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