a. the mean always is the same as the standard deviation

Not at all; could have a negative mean, but standard deviation is always positive

b. the mean is never the same as the mode

Actually, it is

c. the mode is never the same as the median

Actually, it is

Mean, median, and mode are all the same; skew = 0

2. How might the standard deviation (S) of a normal distribution be
greater than the mean?

a. S is given by a square
root, and the square root is larger than the fraction.

What does that have to do with *anything**?*

b. In a normal distribution,
the variance must equal the mean.

Not true, although it is true of a Poisson
distribution (which we didn't get to)

**c.
If some scores are negative, the mean could be very small despite a large
S.**

The
mean could be anything, even negative. Standard deviation is *always
*positive...

d. The median would have
to be less than the skew.

Since the skew of a normal distribution is zero,
this is only true if the mean is negative

3. In a class of 100, the mean on a certain exam was 50, the standard
deviation, 0. This means

a. half the class had scores
less than 50

For the mean to be 50, the others would need scores
above 50. If the scores are not all the same, there will be differences
from the mean; those differences squared will add to a non-zero sum so
standard deviation will be greater than zero.

b. there was a high correlation
between ability and grade

You can't know about correlation from the distribution
of a single variable -- what would it correlate with?

**
c.** **everyone had a score of exactly
50**

A
zero standard deviation means all scores are the same, and equal to the
mean (what else could the mean be?)

d. half the class had 0's
and half had 50's

That would make the mean = 25, and the standard deviation
> 625 (25 squared for everyone)

4. The null hypothesis in an experiment would be

a. there is a high correlation
between the independent and dependent variables

That could be an expectation, but the null hypothesis
says there is **no effect**

**
b.** **changing the independent variable has no significant effect on
the dependent variable**

That
is, every group (experimental or control or whatever) is a sample of the
same population, even though the groups are differentiated by the independent
variable.

c. changing the dependent
variable causes a significant change in the independent variable

That's the opposite of the null hypothesis

d. the standard error of
the dependent variable is greater than the mean of the independent variable

Isn't it amazing how random words in random order
can sound like they mean something?

5. Suppose the mean on the final exam is 24 (of 40), with a standard
deviation of 1.5. If you get a 21, how well do you do (relative to
the rest of the class)?

** a.
very poorly--perhaps the lowest score**

That's
2 standard deviations below the mean (z = -2.0). The fraction in the lower
tail is 0.0228 only 2 1/4% did worse! (Assume
it's roughly a normal distribution....)

b. not well, but somewhere
in the C's

If only 2 1/4% did worse, there won't be many D's or E's, will there?

c. OK--about average

Average is a z near 0

d. nicely--better than the
median

Assuming an approximately normal distribution, median
is close to the mean...

6. You can claim that there is a significant difference between scores
from two groups if

** a.**
**the difference between the means is large compared to the standard error**

This
is basically the definition of *t* (difference in means divided by
standard error). A large *t* means you
can reject the null hypothesis.

b. the means are large compared
to the standard error

Size of means is irrelevant -- it's the difference
that matters. You can't claim two groups differ if their means are the
same, even if the means are 1,000,000 and standard errors are around 0.5.

c. the means are small compared
to the standard error

As in (b) -- it's the **difference** between the means that matters

d. the difference between
the standard deviations is large compared to the means

That's backwards -- it's difference between means,
not standard deviations....

7. The correlation between a person's hair length and score on the midterm
is very nearly zero. If your friend has a crewcut, your best guess
as to what he got on the midterm is

a. the standard deviation
of scores on the midterm

Why would standard deviation predict a score? The
distribution of GRE scores has a mean of 500 and standard deviation of
100 -- 100 is not even a *possible* score!

b. the mean minus the standard
deviation

Even less sensible that (a)

c. the mean plus the standard
deviation

Same as (b)

** d.
the mean score**

If
correlation is zero, there is **no** added information from the other
variable (hair length. Your best guess is the Expected Value, or the mean.

8. There is a low (but real) negative correlation between the amount
of rain in a given summer and the amount the summer before. In the
absence of any information except that this summer is wetter than
usual, you are asked to guess next summer's rain. Your best guess:

a. somewhat more than the
average summer rainfall

Negative correlation means you expect *less*

b. the average summer rainfall

Correlation was real (different from 0) so regression
will do better than the mean

**
c.** somewhat less than the average summer
rainfall

Since the correlation
is negative, more rain this year means less next. The correlation is weak
(small), so the regression line has a low slope; that is, it won't be very
different from the mean.

d. the standard deviation
of the rainfall

A real nonsense answer.

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