1. You have drawn a random sample of size n from a specified population
and
you test the null hypothesis: “population mean = 50”. Suppose that you
are unable to reject the null hypothesis. Your correct interpretation
of the outcome is that
a. for the population, “population mean = 50”.
b. probability is high that for the population, “population mean =
50”.
c. the sample data are not inconsistent with the hypothesis that for
the population, “population mean = 50”.
d. all of the above are acceptable interpretations.
2. The SD of a large population is 20.
H0:
 = 4
vs.
HA:
To test:
 > 4
at level of significance .05, a sample of size 100 will be taken.
You will reject H0 if:
(a)
(c)
3. A result
This means:
a. the
b. the
c. the
d. all
x >= 7.3
x >= 7.8
(b)
(d)
x >= 7.3 or x <= .8
none of the above
was said to be statistically significant at the 5% level.
null hypothesis is probably wrong
result would be unexpected if the null hypothesis were true
null hypothesis is still probably true
of the above.
4. Indicate which assumptions are needed to use the sample mean and normal
tables to test a hypothesis about a population mean and known SD. Which
of the following assumptions are needed to use x , the mean of the data,
and normal tables to test a hypothesis about  ?
I. the data are a random sample
II. the population distribution is normal
III. the sample size is large
a. I, II, and III
b. I and either II or III
c. II and III
d. none of the above
5. For a certain normally distributed population, the value of the
standard
deviation is known, but the value of the mean is unknown. What will be
the effects of changes in sample size and in the confidence level on the
length of the (regular two-sided) confidence interval of the population
mean?
a. Increasing sample size increases the length, given a fixed
coefficient.
b. Increasing the confidence coefficient decreases the length given a
fixed sample size.
c. Increasing sample size decreases the length, given a fixed
coefficient.
d. None of the above
6. In a 95% confidence interval for the mean,
a. if many samples are drawn, a sample average will fall within the
confidence interval 95% of the time.
b. the probability of a sample average falling within a confidence
interval
computed from one sample is .95.
c. the probability of the population mean falling within a confidence
interval computed on one sample is .95.
d. if many samples are drawn, the computed confidence intervals will
contain the population mean 95% of the time.
7. In interval estimation of a population mean, the width of
theinterval can be narrowed by
a. increasing n.
b. lessening the confidence level (e.g., .99 to .90).
c. reducing the magnitude of SD.
d. all of the above.
8. The Central Limit Theorem tells us that:
a) the shape of all sampling distributions of sample means are normally
distributed.
b) the mean of the distribution of sample means is less than the mean
of the parent population.
c) the standard deviation of the distribution of sample means is the
same as the standard deviation of the population.
d) none of the above are true.
9. Consider simple random sampling from a normal distribution with mean
18 and variance 36. For samples of size 9, the sampling
distribution
for the sample mean has mean and variance equal to:
a. 2 and 12 respectively
b.
c.
d.
18 and 4 respectively
18 and 12 respectively
12 and 4 respectively
10. Let X be a random variable with the following probability
distribution:
P(X = 0) = .4
P(X = 1) = .3
P(X = 2) = .2
P(X = 3) = .1
A random sample of 5 values is taken from a population with the
above
probability distribution.
E(sample average) = __________.
SD(sample average) = __________.
11. Assume that commuting time via bicycle to the campus is a normal
random variable with mean mean = 8 minutes and SD = 2 minutes.
If 91% of the bike-commuters take longer to reach campus than you
do, then your commuting time is approximately:
(a) 5.32
(d) 10.68
(b) 5.71
(e) 4.88
(c) 7.54
12. A new diet for the reduction of cholesterol is introduced. In order
to test this procedure, nine patients on this new diet had observed
cholesterol levels of:
patient
cholesterol
patient
cholesterol
1
240
6
220
2
290
7
190
3
220
8
230
4
250
9
200
5
260
sample mean = 210
SD = 30.9
Assume cholesterol levels are normally distributed.
This new method of cholesterol reduction was used on a sample from
a population with a mean cholesterol level of 225. Test the hypothesis
that the procedure used was effective (ALPHA = .05).
a.
H(O): _______________.
b.
c.
d.
e.
f.
H(A): _______________.
test statistic = _______________.
critical region = _______________.
Does the test statistic (c) fall in the critical region (d)?
Conclusion?
13. Suppose in a sample of 25 people, the mean height was observed
to be 70 inches. Suppose also SD = 3.
A. Construct a 95% confidence interval for population mean.
B. Would you reject the hypothesis H(0): population mean = 71
versus H(A): population mean =/= 71 on the basis of the
observations,
when testing at level .05?
C. Would you reject the hypothesis H(0): population mean = 72
versus the alternative H(A): population mean =/= 72 on the basis of
the
observations, when testing at level.05?
D. Would you reject the hypothesis H(0): population mean = 71
versus H(A): population mean =/= 71 on the basis of the observations,
when testing at level .10?
14. True or False? If False, correct it.
The law of large numbers makes it possible to predict long run
relative frequencies but not particular chance events.