STAtistics / Mr. Hansen
12/16/2010

Name: _________________________
Battery bonus (1 pt. for 4 AAA cells): ________
Estimate of score on 12/16 test: _______

Test through Chapter 8 (Calculator Required)

 

Rules
  • You may not write calculator notation anywhere unless you cross it out. For example, terms like binompdf and normalcdf may result in small point penalties. Use diagrams and/or formulas to justify your answers instead.
  • Adequate justification is required for free-response questions.
  • All final answers in free-response portions should be circled or boxed.
  • Decimal approximations must be correct to at least 3 places after the decimal point, and preferably should contain at least 3 significant digits.

 

 

Part I

Notation and Definitions.

 

 

1.

What is Chapter 8 about (2 words)? __________________________________

 

 

 

Write a short paragraph of explanation to make it clear that you know what you are talking about. Define the two symbols, as well as the two words you wrote above.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.

The [imagine inserting 2 words from the blank above] of the sample proportion has a true distribution that is _____________________ . However, if the three _______ of ________ are satisfied, then we can use the _____________ curve as a good approximation.

 

 

3.

Any binomial distribution in which p = 0.5 is symmetric   skew right   skew left
[circle one].

 

 

4.

State the CLT.

 

 

 

 

 

 

 

 

 

 

5.

CLT stands for ____________  ____________  ____________ .

 

 

6, 7.

Explain two major dangers in applying the CLT. (Hint: One of them has to do with using too small a sample size.)

 

Part II

Computation.

 

 

8.

Explain why, in the real world, we would never know the true value of  for a study that involved finding the mean increase in freedom of motion among patients who could be prescribed a certain arthritis medication.

 

 

 

 

 

 

 

 

 

 

 

 

9.

Assume, contrary to reality, that  = 2.9 cm for the situation described in #8. If 45 subjects in the experimental group (as opposed to the control group) are tested, and if the true population s.d. is 1.8 cm, compute the probability that the sample mean for these 45 subjects will be more than 3 cm. Use correct notation and show adequate work. Important: Remember to justify why your approach is valid.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10.

Joe Shilabotnick has an unfair coin that is weighted in such a way that the true proportion of heads it generates is 0.6 instead of 0.5. In 50 flips of this unfair coin, what is the probability that the coin shows 54% or fewer heads? Use the z technique that was discussed in class and taught in the textbook. Important: Be sure to justify—thoroughly—your use of the z technique.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

11.

Work #10 again by using the true sampling distribution of the relevant statistic. Your answer should be quite close to what you obtained in #10.