Which in turn means we cannot support h 1 this means

which, in turn, means we cannot support H
1
. This means there is insufficient evidence to conclude that
the unknown population mean is different than 10.
3. (B). The 95% confidence interval [10.4, 11.2] does not contain the hypothesized value of 10. This means
we reject Ho which, in turn, means we support H
1
. This means there is sufficient evidence to conclude
that the unknown population mean is different than 10.
4. (D). The 95% confidence interval [9.8, 10.4] contains the hypothesized value of 10. This means we
cannot reject Ho which, in turn, means we cannot support H
1
. This means there is insufficient evidence
to conclude that the unknown population mean is different than 10.
Note : the burden of proof is always on H
1
so we always say “ insufficient evidence exists to conclude H
1
…”
when we do not reject Ho. We always say “ sufficient evidence exists to conclude H
1.
..” when we reject Ho.
We never conclude that something is exactly equal to a hypothesized value (since equality is always in the
null hypothesis which is always rejected or not rejected, but it is never supported or taken to be true).
Jury Trial Example : Ho: Defendant is innocent, H
1
: Defendant is guilty. The jury decision is either
“sufficient evidence exists to find the defendant guilty” (if Ho is rejected) or “insufficient evidence exists to
find the defendant guilty” (if Ho is not rejected). The defendant is never found innocent, just not guilty.
5. (B). Type I error is a “false alarm”, which is the smoke detector sounding when there’s not really a fire.
6. (A). Power is the probability of the smoke detector sounding when there really is a fire. Also, Power = 1
– Probability(Type II Error), where a Type II error is a “missed alarm” (i.e., smoke detector not sounding
when there really is a fire).
7. (A). The sample mean
x
is always in the center of a confidence interval, since a confidence interval is
developed by taking the sample mean
x
(which is a point estimate of the unknown population mean) and
then subtracting the margin of error to get the lower confidence interval value and adding the margin of
error to get the upper confidence interval value.
8. (C). Type I error and Type II error probabilities move in opposite directions (all else equal). So if the
probability of a Type I error goes up, the probability of a Type II error will go down (all else equal).
Think of a smoke detector: if we make it more sensitive (easier to go off), the probability of a false alarm
(Type I error) will increase but the probability of a missed alarm (Type II error) will decrease.
9. (B). By definition, the level of significance represents the probability of a Type I error. So if α = 0.01,
this means the probability of a Type I error = 0.01.
10. (D). Increasing sample size will reduce the width (increase the precision) of a confidence interval. Just

examine the confidence interval formula to see why this has to be true. Answer choices B & C actually
increase the width of a confidence interval. Answer choice A (sample mean) has nothing to do with the
width of a confidence interval.