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AP Statistics / Mr. Hansen |
Name: _________________________ |
Quiz
on Chapter 10 and Recent Class Discussions
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1. |
A _________ _______________
is the set of all possible values that a statistic can have when samples of a
fixed size are drawn from a fixed population. Although we could consider
__________ distributions for many statistics (s, Q1,
range, IQR, etc.), the two
statistics of greatest interest to us in ___________ distributions are ____
(the sample mean) and _______ (the sample ________________
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2. |
If a large dataset has a
mean of 83 and a s.d. of
5, then the sample means, using samples of size 55, will have a _______ of 83
and a _______ of .674. |
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3. |
If 35% of a large
population are “yeses” and 65% are “no’s,” then the sample proportion of
“yeses,” using samples of size 55, will have a mean of ___________ and a s.d. of _________ . The count of “yeses” in samples of size 55
will have a mean of ___________ and a s.d. of
_________ . |
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4. |
In an SRS of 1350 American
voters, 713 give President Bush a “positive” job approval rating. Compute a
95% confidence interval for the true proportion of American voters who feel
this way. No work is required, but state your answer
as a complete sentence using the “approved wording” that we discussed in
class. |
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5. |
We measure the heights of
1000 randomly selected American women. A 90% confidence interval for the mean
height of American women is 65 ± .13 inches. Which of the following are true? (Write
the word “YES” in front of each true statement.) |
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The probability is .9 that
the true mean height of American women lies in the interval
between 64.87 and 65.13 inches. |
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The probability is .9 that
the true mean height of American women lies in the
interval from 64.87 through 65.13 inches, inclusive. |
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If we performed the
randomization and measurement procedures again, there is a probability of .9
that the true mean height of American women would fall in the interval from
64.87 to 65.13. The issue of “inclusive” or “non-inclusive” is irrelevant
since the r.v. is continuous. |
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If we performed the
randomization and measurement procedures again and computed a new confidence
interval, there is a probability of .9 that the true mean height of American
women would fall in the new interval. The issue of “inclusive” or
“non-inclusive” is irrelevant since the r.v. is
continuous. |
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We are 90% confident that
the true mean height of American women is 65 ± .13 inches. |
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Approximately 90% of
American women have heights between 64.87 and 65.13 inches. |
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6. |
In problem #5, compute the m.o.e. for a 99% confidence level. (Hint: s = 2.5 inches.) This time, show your work. |
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7. |
Mel, who has many tall
female friends, believes based on his anecdotal experience that the estimate of
65 inches given in problem 5 is too low. State Mel’s null and alternative
hypotheses for the true mean height of American women: |
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(a) |
H0: ______________________________ |
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(b) |
Ha:
______________________________ |
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(c) |
Mel will gather his own large
random sample of women and will measure their heights. He will reject H0 if the p value of his test is below .05.
Explain in plain English what a Type I error by Mel would be. |
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(d) |
State the probability that Mel
makes a Type I error (no work needed). |
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(e) |
Explain in plain English
what a Type II error by Mel would be. |
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(f) |
Explain in plain English
why it is not possible to compute P(Type II error) unless Mel tells you a specific alternative sampling
distribution that he has in mind. |
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(g) |
Two specific alternatives
Mel is considering are m = 66 and m = 67 inches. Against which of these alternatives does Mel’s procedure
have greater power? Explain briefly. |
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