STAtistics / Mr. Hansen
4/20/2011

Name: _________________________
Battery bonus (Mr. Hansen’s use only): _____

Cumulative Test
You can get up to an A++ (108%) if you answer all questions and have spare batteries.

 

 

 

Part I: Straight from the MPQ (5 pts. each)

 

 

 

 

1.

What does MSE mean? Is it a synonym for variance?

 

 

 

 

 

 

 

 

 

 

2.

Tell whether the following regression-related terms are synonyms: ____________ outlier and ____________ observation. If not, why not?

 

 

 

 

 

 

 

 

 

 

 

 

 

3.

What name do we give to r2? What does r2 mean?

 

 

 

 

 

 

 

 

 

 

 

 

4.

Interpret b0 and b1 for a layperson.

 

 

 

 

 

 

 

 

 

 

5.

What do the letters r.v. mean? Give two examples, one that is ____________ and another that is ____________ .

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6.

Random variables: The variance of a ____________ equals the ____________ of the ____________ . Is this always true? ____ What about for differences?

 

 

 

 

 

 

 

 

 

 

 

 

 

7.

What does CLT stand for? ________________________ State it correctly and in one of the many ways in which people misconstrue it.

Correct: __________________________________________________________

 

 

 

 

 

Incorrect: __________________________________________________________

 

 

 

 

8.

In your own words, define P-value and describe how it is determined or computed.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Part II: Straight from the AP formula sheet (5 pts. each)

 

 

 

 

9.

In a LSRL data set, the mean explanatory variable value is 7.2, and the mean response variable value is −8.1. Calculate the intercept if the slope is −4.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10.

A C.I. can be expressed in the format of statistic  ____________________ . Fill in the blank with the term we learned, not the formula from the formula sheet.

 

 

 

 

11.

On page 3, formula 5 is for a ________________________________________ , whereas formula 6 is for a __________________________________________ (usually).

 

 

 

 

12.

Translate the formula  found near the middle of page 2, into English: The expected value of the ___________________ equals the ___________________ , or in other words,  is an _____________________________________ of p.

 

 

 

 

13.

Compute  if n = 35 and q = 0.2.

 

 

 

 

 

 

 

 

 

 

14.

A spinner with equally sized regions for 1, 2, 3, and 4 is spun once, and the random variable Q is used to denote the value of the spin. Compute the mean and variance of Q. Work is optional, but there is no partial credit if you are wrong and have shown no work.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

15.

In western North Dakota, the probability of rain is 0.25, and the probability of high wind is 0.8. The probability of at least one of the two (i.e., rain or high wind or both) is 0.95. Compute the probability of a rainy day with high wind.

 

16.

A fair coin is flipped 16 times. Compute the probability of obtaining exactly 7 heads. Work is optional, but again, there is no partial credit if you are wrong and show no work.

 

 

 

 

 

 

 

 

 

 

 

 

 

Part III: “Hybrid” problems (5 pts. each)

 

 

17.

Eggs from Joe’s Henhouse have a mean mass of 130 g, with s.d. 11 g. Compute the probability that a carton of a dozen randomly chosen eggs exceeds 1600 g in total. (Hint: Pose the question to yourself in terms of the mean mass per egg, if the total were to exceed 1600 g. Also, assume that egg masses are normally distributed.)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

18.

After a tough winter, Farmer Joe, owner of Joe’s Henhouse, is concerned that his hens are no longer producing eggs with a mean mass of 130 g. He tests the hypotheses

H0:
Ha:

by gathering data from an SRS of 250 eggs. The sample s.d. is 11 g, as expected, but the sample mean is 129 g. Compute the P-value. _________ For the P-value that you found, does Farmer Joe have any evidence that his hens are not averaging 130 g per egg? __________ (Test with .)

 

 

19.

A chi-square test for independence involves two categorical variables: relationship status (single, attached, other) vs. GPA (high, medium, low). If the test statistic equals 11.5, compute or estimate the P-value: __________ Using the  = 0.05 level, write a conclusion in context. No work is expected.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

20.

A LSRL t test on 18 data points (assume all assumptions are met) tests the hypotheses

H0:
Ha:

For this test, df = ______ . If the test statistic equals 2.15, compute or estimate the P-value. ______ (No work is required.)

 

 

21.

When I flip a fair coin 24 times, I expect to obtain ____ heads and ____ tails. If I actually obtain 10 heads and 14 tails, the value of the 2-tailed z test statistic is ___________ , giving a P-value of ____________. (No work is expected.) This compares with a goodness-of-fit test statistic (null hypothesis: phead = ptail = 0.5) of _______________ and P-value of ____________. Please show work below for the second test statistic only.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

BONUS
(2 pts.)

Would the P-values in #21 have matched if the z test statistic were 1-tailed? ____ Why or why not?