Today:
- Announcements:
- We've got an exam coming up Tuesday.
- It will cover through 5.3, but will not include material from 5.2
(proportions). Description is included with this
take-home
portion of the exam (worth 30% of your grade). Any questions on
that?
- You'll be able to use your sheet of important formulas during the exam.
- Make
sure to visit
the sample problem page: test questions are likely to
resemble these, as well as your homework problems.
- Review your quizzes as well.
- Return quiz 6
- mean of 7
- sd of 2.1
- Probabilities are always positive.
- To get percentages from probabilities, multiply by 100.
- In part B, we want you to use the result of part A: you
should refer to the .003 probability (.3%) in your
justification. That's the value in computing the
probability!
- Fair number of you are having a hard time using the
Z-table "backwards".
- Pictures help, and tell you when your answer doesn't make
sense. For example, you should know that the answer is
less than the mean (< 22), since 50% have better gas
mileages than the mean.
- Questions about material, quizzes, homework problems?
- Section 5.2: The Sampling distribution of the Sample Proportion
- Definition: Consider a sample of qualitative data for which
one category, or attribute, is of interest. To describe such a sample, we will
use the proportion of the sample having the attribute of interest. This
statistic is denoted by the letter p.
- Properties of the sampling distribution of the sample proportion:
- The mean of the sampling distribution of p, denoted
, is equal to the mean of the population
.
- The standard deviation of the sampling distribution of p, denoted
, is
where n is the sample size.
- Here's the key thing: the sampling distribution for
p is approximately normal for a large sample size n ("large"
generally taken as greater than or equal to n=30 at the very
least, but in this case it depends as well on the value of
) as well.
- Our choice of n to ensure normality is made so that
three standard errors from the estimated
are completely contained inside the interval [0,1]:
and
- See p. 186 for the strategy
- See Figure 5.7 and 5.8, p. 182-183
- Calculating probabilities for p involves computing
Z-scores, as usual
- Exercise #8, p. 189
- Exercise #5, p. 202
Links
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