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Practice Test
AP Statistics
Name:
Directions: Work on these sheets. Tables and formulas appear on a separate sheet.
Part 1: Multiple Choice. Circle the letter corresponding to the best answer
1. 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
2. In a test of H0: µ = 100 against Ha: µ > 100, a sample of size 80 produces z = 0.8 for the value of
the test statistic. The P-value of the test is thus equal to
(a) 0.20
(b) 0.40
(c) 0.29
(d) 0.42
(e) 0.21
3. A certain population follows a Normal distribution with mean  and standard deviation   22.1.
You collect data on four members of the population and test the hypotheses
H 0 :   100; H a :   100 .
You obtain a P-value of 0.052. Which of the following is true?
(a) At the 5% significance level, you have proved that H 0 is true.
(b) You have failed to obtain any evidence for H a .
(c) There is some evidence against H 0 , and a study using a larger sample size may be worthwhile.
(d) This should be viewed as a pilot study, and the data suggest that further investigation of the
hypotheses will not be fruitful at the 5% significance level.
(e) None of the above.
4. We want to test H0: µ = 1.5 vs. Ha : µ  1.5 at  = 0.05 . A 95% confidence interval for µ
calculated from a given random sample is (1.4, 3.6). Based on this finding we
(a) fail to reject H0 .
(b) reject H0 .
(c) cannot make any decision at all because the value of the test statistic is not available.
(d) cannot make any decision at all because the distribution of the population is unknown.
(e) cannot make any decision at all because (1.4, 3.6) is only a 95% confidence interval for µ.
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Practice Test
5. In hypothesis testing,  is the probability of committing a Type II error. The power of the test,
1   , is then
(a) the probability of rejecting H0 when Ha is true
(b) the probability of failing to reject H0 when Ha is true
(c) the probability of failing to reject H0 when H0 is true
(d) the probability of rejecting H0 when H0 is true
(e) the probability of failing to reject H0.
6. Which of the following is not a required condition for performing a z test about an unknown
population mean  ?
(a) The data can be viewed as a simple random sample from the population of interest.
(b) The population standard deviation  is known.
(c) The population distribution is Normal or the sample size is large (say n > 30).
(d) The data represent n independent observations.
(e) np  10 and n(1  p)  10 .
7. A researcher wishes to determine if students are able to complete a certain pencil and paper maze
more quickly while listening to classical music. Suppose the time (in seconds) needed for high
school students to complete the maze while listening to classical music follows a Normal
distribution with mean  and standard deviation  = 4. Suppose also that, in the general
population of all high school students, the time needed to complete the maze follows a Normal
distribution with mean 40 and standard deviation  = 4. The researcher, therefore, decides to test
the hypotheses
H 0 :   40, H a :   40
To do so, the researcher has 10,000 high school students complete the maze with classical music
playing. The mean time for these students is x = 39.8 seconds. It is appropriate to conclude which
of the following?
(a) The researcher has proved that, for high school students, listening to classical music
substantially improves the time it takes to complete the maze.
(b) The researcher has strong evidence that, for high school students, listening to classical music
substantially improves the time it takes to complete the maze.
(c) The researcher has moderate evidence that, for high school students, listening to classical music
substantially improves the time it takes to complete the maze.
(d) Although the researcher has obtained a statistically significant result, it has little practical
significance.
(e) None of the above.
8. A researcher plans to conduct a significance test at the  = 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 II error for the particular alternative value of the
parameter at which she computed the power is
(a) 0.01.
(b) 0.10.
(c) 0.89.
(d) 0.90.
(e) equal to 1  (P-value) and cannot be determined until the data have been collected.
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Practice Test
Part 2: Free Response
Communicate your thinking clearly and completely.
9. Does the use of fancy type fonts slow down the reading of text on a computer screen? Adults can
read four paragraphs of text in an average time of 22 seconds in the common Times New Roman
font. Ask 25 adults to read this text in the ornate font named Gigi. Here are their times:
23.2 21.2 28.9 27.7 29.1 27.3 16.1 22.6 25.6
34.2 23.9 26.8 20.5 34.3 21.4 32.6 26.2 34.1
31.5 24.6 23.0 28.6 24.4 28.1 41.3
Suppose that reading times are Normal with  = 6 seconds. Is there good evidence that the mean
reading time for Gigi is greater than 22 seconds? Carry out an appropriate test to help you answer
this question.
P
The Parameter of interest is the mean reading speed for fancy fonts on a computer.
H H0:  = 22 The mean reading time for the Gigi font is 22
Ha:  > 22 The mean reading time for the Gigi font is greater than 22
A SRS – not told, proceed with caution
Independent
10(25)< all measurements
Approx Normal – told the reading times are normal ( Note that there is one high outlier of 41.3)
N one sided z- test with  = .05
𝑥̅ −µ
T Z=
𝜎
√𝑛
=
O P(Z > 4.24) = 0
27.088−22
6
√25
= 4.24
(If you removed the outlier, z = 3.75, p = 0)
M Since p = 0 and is less than a = 0.05, we reject the null hypothesis.
S There is not sufficient evidence to suggest that the mean reading time for Gigi is 22.
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Practice Test
10. Emissions of sulfur dioxide by industry set off chemical changes in the atmosphere that result in
“acid rain.” The acidity of liquids is measured by pH on a scale of 0 to 14. Distilled water has pH
7.0, and lower pH values indicate acidity. “Normal” rain is somewhat acidic, so acid rain is
sometimes defined as rainfall with a pH below 5.0. Suppose that pH measurements of rainfall on
different days in a Canadian forest follow a Normal distribution with standard deviation  = 0.5.
You plan to test
H 0 :   5; H a :   5
at the 5% level of significance.
(a) What values of z would lead you to reject H 0 in this setting? Show your method.
In the Z-table, look for the probability to be less than .05. It happens when the z <-1.645.
(b) Describe a Type I and a Type II error in this situation, and give the consequences of each.
A Type I error occurs when you conclude that the mean pH is less than 5 when it really is. In this case
you will state that the rainfall is acidic when it is really not.
A Type II error occurs when you conclude that the pH isn’t less than 5 when it really is, concluding
that the water is “normal” when it is really acidic.
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Practice Test