AP STATISTICS: Warm Up #1
Chapter 9
1. In formulating hypotheses for a statistical test of significance, the null hypothesis is often
A) a statement of “no effect” or “no difference.”
B) the probability of observing the data you actually obtained.
C) a statement that the data are all 0.
D) 0.05.
E) the probability that the parameter value is actually µ.
2. To determine if having children within the first two years of marriage increases the divorce rate, where
p = proportion of marriages that end in divorce, we should test the hypotheses
A) H 0 : pˆ  0.5; H a : pˆ  0.5
B) H 0 : pˆ  0.5; H a : pˆ  0.5
C) H 0 : p  0.5; H a : p  0.5
D) H 0 : p  0.5; H a : p  0.5
E) H 0 : p  0.5; H a : p  0.5
3. The average growth of a certain variety of pine tree is 10.1 inches in three years. A biologist claims that
a new variety will have a greater three-year growth. A random sample of 25 of the new variety has an
average three-year growth of 10.8 inches and a standard deviation of 2.1 inches. The appropriate null and
alternative hypotheses to test the biologist's claim are
A) H0: µ = 10.8 against Ha: µ > 10.8
B) H0: µ = 10.8 against Ha: µ  10.8
C) H0: µ = 10.1 against Ha: µ > 10.1
D) H0: µ = 10.1 against Ha: µ < 10.1
E) H0: µ = 10.1 against Ha: µ  10.1
.
4. The P-value of a test of a null hypothesis is the probability that
A) assuming the null hypothesis is true, the test statistic will take a value at least as extreme as that
actually observed.
B) assuming the null hypothesis is false, the test statistic will take a value at least as extreme as that
actually observed.
C) the null hypothesis is true.
D) the null hypothesis is false.
E) the alternative hypothesis is true.
5. In testing hypotheses, which of the following would be strong evidence against the null hypothesis?
A) Using a small level of significance
B) Using a large level of significance
C) Obtaining data with a small P-value
D) Obtaining data with a large P-value
E) Obtaining data with a low test statistic
6. I conduct a statistical test of hypotheses and find that the my results are statistically significant at
level  = 0.05.
I may conclude that
A) the test would also be significant at level  = 0.10.
B) the test would also be significant at level  = 0.01.
C) the P-value is less than .05.
D) both (A) and (C) are true.
E) both (B) and (C) are true.
AP STATISTICS: Warm Up #2
Chapter 9
1. In tests of significance about an unknown parameter of some population, which of the following is
considered strong evidence against the null hypothesis?
A) The value of an estimate of the unknown parameter based on a simple random sample from the
population is not equal to zero.
B) The value of an estimate of the unknown parameter lies within 2 units of the sample value.
C) We observe a value of an estimate of the unknown parameter based on a simple random sample
from the population that is very consistent with the null hypothesis.
D) We observe a value of an estimate of the unknown parameter based on a simple random sample
from the population that is very unlikely to occur if the null hypothesis is true.
E) The value of an estimate of the unknown parameter based on a simple random sample from the
population is equal to zero.
2. A test of significance produces a P-value of 0.024. Which of the following conclusions is appropriate?
A) Accept Ha at the  = 0.05 level
B) Reject Ha at the  = 0.01 level
C) Fail to reject H0 at the  = .05 level
D) Reject H0 at the  = 0.05 level
E) Accept H0 at the  = 0.01 level
3. If we reject the null hypothesis when, in fact, it is true, we have
A) committed a Type I error.
B) committed a Type II error.
C) a probability of being correct that is equal to the P-value.
D) a probability of being correct that is equal to 1 – P-value.
E) set the  level too high.
4. A researcher plans to conduct a test of hypotheses at the 𝛼 = 0.01 significance level. She designs her
study to have a power of 0.90 at a particular alternative value of the parameter of interest. The probability
that the researcher will commit a Type I error is
A) 0.01. B) 0.10.
C) 0.89.
D) 0.90.
E) equal to the P-value and cannot be determined until the data have been collected.
5. In testing hypotheses, if the consequences of incorrectly rejecting the null hypothesis are very serious,
we should
A) use a very large level of significance.
B) use a very small level of significance.
C) insist that the P-value be smaller than the level of significance.
D) insist that the level of significance be smaller than the P-value.
E) consult with an expert in the field you're studying for an interpretation of the P-value index.
6. The power of a statistical test of hypotheses is
A) the smallest significance level at which the data will allow you to reject the null hypothesis.
B) equal to 1 − (P-value).
C) the probability that the test will reject both one-sided and two-sided hypotheses.
D) the probability that a significance test will reject the null hypothesis when a particular alternative
value of the parameter is true.
E) equal to 1 − P (Type I error).
AP STATISTICS: Warm Up #3
Chapter 9
1. Which of the following will increase the power of a statistical test of significance.
A) Increase the Type II error probability.
B) Increase the sample size.
C) Reject the null hypothesis only if the P-value is smaller than the level of significance.
D) Decrease the 𝛼 level.
E) All of the above.
Use the following for questions 2-3
A December 2007 Gallup Poll reported that 43% of Americans use the internet for an hour or more each
day. You suspect that a higher proportion of students at your school use the internet that much. To find
out, you take a simple random sample of 60 students and find that 35 of them use the internet for an hour
or more each day. (Assume your school has enough students so that this is a small sample relative to the
size of the population). You will test the hypotheses H 0 : p  0.43; H a : p  0.43 , where p = the proportion
of students at your school who use the internet for an hour or more each day, at the
𝛼 = 0.01 level.
2. Which of the following best describes the sampling distribution of proportions for this test?
A) Mean = 0.583; Standard deviation = 0.064; shape approximately Normal
B) Mean = 0.583; Standard deviation = 0.064; shape unknown
C) Mean = 0.5; Standard deviation = 0.064; shape approximately Normal
D) Mean = 0.43; Standard deviation = 0.064; shape approximately Normal
E) Mean = 0.43; Standard deviation = 0.064; shape unknown
3. The test statistic, P-value, and appropriate decision for this test are:
A) z = 2.40; P-value = 0.008; reject Ho
B) z = 2.40; P-value = 0.008; fail to reject Ho
C) t = 2.40; P-value = 0.0103; reject Ho
D) t = 2.40; P-value = 0.0103; fail to reject Ho
E) no conclusion can be drawn, because the shape of the sampling distribution is unknown.
4. In 1999, 2.2% of all cars in the United States were reported stolen. In a random sample of 400 Nissan
Maxima cars that year, 12 were reported stolen. Is this evidence (at the 𝛼 = 0.05 level) that the theft rate
for this model is higher than the national rate?
A) Yes, the P-value = 0.1377, so we reject H0 and conclude that the rate for Nissans is higher that
2.2%.
B ) No, the P-value = 0.1377, so we fail to reject H0 and cannot conclude that the rate for Nissans is
higher that 2.2%.
C) Yes, the P-value = 0.1685, so we reject H0 and conclude that the rate for Nissans is higher that
2.2%.
D) No, the P-value = 0.1685, so we fail to reject H0 and cannot conclude that the rate for Nissans is
higher that 2.2%.
E) We cannot perform this test because the conditions for inference have not been met.
AP STATISTICS: Warm Up #4
Chapter 9
1. Ten years ago, the mean Math SAT (SAT-M) score of all high school students who took the exam at a
small high school was 490 with a standard deviation of 80. A boxplot of the SAT-M scores of a random
sample of 25 students at the same high school who took the exam this year is given below. The mean
score of these 25 students is x  530 and the standard deviation is s  69.5 . To determine if there is
evidence that the average SAT-M score in the district has improved, the hypothesis H0: µ= 490 is tested
against the alternative Ha: µ > 490 and the P-value is found to be 0.0037.
We may conclude that
A) at the 5% significance level, we have convincing evidence that H0 is false.
B) at the 5% significance level, we have convincing evidence that Ha is false.
C) at the 5% significance level, we have convincing evidence that H0 is true.
D) it would have been more appropriate for us to use a two-sided alternative.
E) none of the above is true, because the conditions for this procedure have not been met.
2. The most important condition for sound conclusions from statistical inference is usually
A) that the population standard deviation is known.
B) that at least 30 people are included in the study.
C) that the data can be thought of as a random sample from the population of interest.
D) that the population distribution is exactly Normal.
E) that no calculation errors are made in the confidence interval or test statistic.
3. I draw an SRS of size 15 from a population that has a normal distribution with mean µ and standard
deviation σ. The one-sample t statistic
x 
has how many degrees of freedom?
s
15
A) 15
B) 14
C) 15
D) We cannot determine the degrees of freedom without knowing the value of s.
E) 0; the population standard deviation is known.