|
AP Statistics / Mr. Hansen |
Name: _________________________ |
AP
Free-Response Practice I (100 points)
|
|
Instructions: Show adequate justification for each answer. |
|||||
|
|
|
|||||
|
1.(a) |
Explain briefly why, in a linear regression
t test, testing for the alternative
hypothesis that the true slope is positive is equivalent to testing for the
alternative hypothesis that the true r
value (usually called r) is positive. |
|||||
|
|
|
|||||
|
|
|
|||||
|
|
|
|||||
|
|
|
|||||
|
|
|
|||||
|
|
|
|||||
|
|
|
|||||
|
|
|
|||||
|
|
|
|||||
|
(b) |
Determine the true expected probabilities
and counts that would occur if the data shown below had come from a normal
distribution with mean 500 and s.d. 100. No work is
required. |
|||||
|
|
|
|||||
|
|
(from
297 randomly chosen SAT math scores) |
|||||
|
|
|
|
|
|
|
|
|
|
|
score
< 350 |
|
20 |
|
|
|
|
|
350 £ score < 475 |
|
100 |
|
|
|
|
|
475 £ score < 575 |
|
115 |
|
|
|
|
|
score
³ 575 |
|
62 |
|
|
|
|
|
|
|
_______ |
|
|
|
|
|
|
|
297 |
|
|
|
|
|
|||||
|
(c) |
Perform a goodness-of-fit test to assess
whether the data above might have come from a normal distribution with mean
500 and s.d. 100 (the null hypothesis) or from some
other type of distribution (the alternative). You must state and verify
assumptions for full credit. |
|||||
|
2. |
The FloatFloat.com competition in May had 778
possible chances to win. The 45 student contestants had between 1 and 32
chances each, and 6 winners were randomly chosen. |
||||
|
|
|
||||
|
(a) |
Explain why a simulation is the most
appropriate method fro computing a student’s probability of being a winner. |
||||
|
|
|
||||
|
|
|
||||
|
|
|
||||
|
|
|
||||
|
|
|
||||
|
|
|
||||
|
|
|
||||
|
(b) |
In a simplified contest in which the 45
contestants each have 1 chance to win (i.e., 45 total numbers, instead of
778), compute the probability that a given student (Max) is one of the 6
winners. |
||||
|
|
|
||||
|
|
|
||||
|
|
|
||||
|
|
|
||||
|
|
|
||||
|
|
|
||||
|
|
|
||||
|
(c) |
Describe but do not execute a simulation to estimate the probability that Max
is one of the 6 winners in the real
FloatFloat contest. Max has 32 chances to win, and
notional (fake) data are shown below. |
||||
|
|
|
||||
|
|
|
Student |
# of chances |
|
|
|
|
|
Sharpe |
1 |
|
|
|
|
|
Shoes |
1 |
|
|
|
|
|
Armstrong |
15 |
|
|
|
|
|
Baker |
16 |
|
|
|
|
|
Clark |
14 |
|
|
|
|
|
· |
· |
|
|
|
|
|
· |
· |
|
|
|
|
|
· |
· |
|
|
|
|
|
Lemi |
22 |
|
|
|
|
|
Max |
32 |
|
|
|
|
|
|
_______ |
|
|
|
|
|
Total |
778 |
|
|