AP Statistics Test Errors and Hypothesis
Testing
 For a two tailed test with a p=.02, What is the area
under the curve associated with p in one of the tails?
Area = 0.01
 If a confidence interval is tripled, what is the effect
on the margin of error? tripled
 If the sample size is increased by a factor of 16, what
is the effect on the margin of error? 1/4 times
original ME
 If the confidence level is changed from 90% to 95% what
is the effect on the margin of error? (1.96 /
1.64) times ME or a 19% increase in ME
 What conditions must be met in order to use a ttest?
SRS, population approximately normally
distributed
 For a given test of statistical significance alpha =
.02 and the pvalue = .025. What can you conclude?
There is not a statistically significant reason to
reject the null hypothesis
 Juan obtains a pvalue = .018 in his significance test.
How should he interpret it? There is an 1.8%
probability of getting a value of the test statistic as extreme or more
extreme than the one obtained.
 A two tailed quality assurance test has an alpha = 5%.
What is the probability of a type I error?
5%
 Which hypothesis is assumed to be true when evaluating
the probability of a type I error? the null
hypothesis
 What is the sum of the probability of a type I and type
II error for a given set of circumstances?
Unknown
 What is the sum of the probability of a type II error
and power for a given set of circumstances? 1.00
 When is a pooled ttest used?
When the standard deviations of the 2
samples are considered to be equal
 In the American justice system, the presumption of
innocence until proven guilty can be called the _________________.
null hypothesis
 For a hypothesis test beta = 10%. What is the power of
the test? 90%
 Martha plans a survey and wants a margin of error of 2%
with a confidence level of 95%. What is the minimum sample size she should
use? n = 2401
 Based on a survey of 1600 people, Bob finds that 60%
will vote for the purple party. Construct a 95% confidence interval for
the data.
CI = 0.6 ± 1.96 [ .6 (1.6))/
1600]^0.5 or .6 ± 0.24
 Based on sample of 1000, SC voters vote purple 45% of
the time while based on a sample of 1200 voters, GA voters vote purple 49%
of the time. Construct a 90% confidence interval for the difference
between the two groups. ( 0.075
to 0.0049)
 A sample of Martha's coconuts has an average weight of
1.3 lb with a sample size = 12 and s = 4. A sample of Bob's coconuts has
an average weight of 1.5 lb with a sample size = 10 and s = 3. Are Bob's
coconuts bigger than Martha's? p
= 44.7%
 Create a 80% confidence interval for the difference
between Bob's and Martha's coconuts. (2.18 to
1.78)
 What does the central limit theorem tell us about the
effects of sample size on the sampling distribution?
As sample size increases, the sampling distribution
narrows and looks more like a normal distribution
 What 2 conditions must be true to use the normal
approximation of the binomial? np
>= 10, n(1p) >= 10
