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AP Statistics Medium practice

15 questions

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Medium practice

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Question 1

A scatterplot of two variables shows a strong curved relationship. A student computes $r = 0.45$ and concludes the association is weak. What is the error in the student's reasoning?

A.The student should use

r^{2}

instead of

r

to assess strength.B.

r

measures only the strength of the linear association; a low

r

with a curved pattern means the relationship is strong but non-linear.C.The student should use Spearman's rank correlation for curved data.D.A value of

r = 0.45

can still indicate a strong relationship.

Question 2

A paired $t$ -test produces $\overset{ˉ}{d} = 5.2$ , $s_{d} = 7.1$ , $n = 18$ . Compute the $t$ statistic for testing $H_{0} : μ_{d} = 0$ vs. $H_{a} : μ_{d} > 0$ .

t \approx 0.73

t \approx 3.11

t \approx 3.56

t \approx 1.67

Question 3

Two sampling distributions are described: (I) $n = 25$ samples from a symmetric, bell-shaped population; (II) $n = 100$ samples from a heavily skewed population. Which is more likely to be approximately normal?

A.Distribution I, because the population is symmetric.B.Distribution II, because

n = 100

is large enough by the CLT even for skewed populations.C.Both are equally normal, because the CLT applies in both cases.D.Neither is approximately normal, because neither comes from a perfectly normal population.

Question 4

A dot plot shows the ages (in years) of 9 trees: 3, 5, 5, 7, 8, 9, 10, 12, 40. Which measure of center best represents the typical age, and why?

A.Mean, because it uses all values in the data set.B.Median, because it is resistant to the extreme value of 40.C.Mean, because it equals the median in symmetric distributions.D.Mode, because 5 appears twice.

Question 5

A researcher conducts a chi-square test of independence with $χ^{2} = 15.3$ , $df = 4$ , $p < 0.01$ . A student says the test shows that column variable $B$ causes changes in row variable $A$ . What is the error?

A.The test only shows association, not direction; which variable causes the other cannot be determined.B.Chi-square tests measure association, not causation; without an experiment, causal conclusions are not justified.C.A

p

-value < 0.01 is not small enough to conclude association.D.The

df = 4

is too small for a valid chi-square test.

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Question 6

A sample of $n = 50$ is taken from a large population where $p = 0.20$ . A student checks the conditions for using a normal approximation and finds $n p = 10$ , $n (1 - p) = 40$ . The student concludes the approximation is barely acceptable. Is this correct?

A.No; the condition requires

n p > 10

strictly, so

n p = 10

fails.B.Yes; both

n p \geq 10

and

n (1 - p) \geq 10

are satisfied, so the normal approximation is justified.C.No; the condition also requires

n \geq 30

, which fails here.D.No; for a proportion, the sample size must be at least 100.

Question 7

A chi-square goodness-of-fit test is performed on a spinner with 3 sections claimed to be equally likely. The test statistic is $χ^{2} = 5.4$ with $df = 2$ . The $p$ -value is approximately 0.067. At $α = 0.05$ , is there evidence the spinner is unfair?

A.Yes;

χ^{2} = 5.4

is large, so the spinner is definitely unfair.B.No;

p

-value = 0.067 >

α = 0.05

, so we fail to reject the null hypothesis that the spinner is fair.C.Yes; any

χ^{2} > 5

with small

df

indicates a significant result.D.No; the

p

-value should be doubled for a two-sided test.

Question 8

The $p$ -value for a one-sided test is 0.03. Which of the following is a correct interpretation of this $p$ -value?

A.There is a 3% probability that

H_{0}

is true.B.If

H_{0}

were true, there is a 3% probability of obtaining a test statistic at least as extreme as the one observed.C.There is a 97% probability that the alternative hypothesis is correct.D.The data support

H_{0}

with 97% confidence.

Question 9

A residual plot for a regression of price on square footage shows a fan-shaped pattern (residuals get larger as $x$ increases). What condition is violated, and what does this mean for inference?

A.Linearity is violated; the relationship is not linear.B.Equal variance is violated; inference on the slope may be unreliable.C.Normality is violated; the residuals are skewed.D.Independence is violated; the data have a time-trend.

Question 10

A survey asks: "Do you agree that the city council wastes taxpayer money on unnecessary projects?" What problem does this question have?

A.The question does not use a random sampling method.B.The question is too short to collect meaningful data.C.The question is leading and will likely produce response bias toward agreement.D.The question is subject to nonresponse bias.

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Question 11

An experiment randomly assigns participants to one of three diets. After 8 weeks, mean weight loss is compared across groups. Which principle of experimental design ensures that unmeasured variables (like initial metabolism) are evenly distributed among the groups?

A.ReplicationB.ControlC.Random assignmentD.Blinding

Question 12

Conditions for a one-sample $t$ -test include randomness, independence (10% condition), and normality. A sample of $n = 8$ shows a slightly skewed dotplot with no outliers. Is the normality condition met?

A.No;

n = 8 < 30

, so normality cannot be assumed by the CLT.B.Yes; slight skew with no outliers in a small sample is considered acceptable for the

t

-procedure.C.No; the

t

-procedure always requires

n \geq 30

.D.Yes; the

t

-procedure is valid for any sample distribution.

Question 13

A biology class recorded the number of seeds that germinated out of 20 seeds for each of 30 students. The data are roughly bell-shaped with mean $\overset{x}{ˉ} = 14.2$ and $s = 2.1$ . Using the normal model, approximately what proportion of students had fewer than 10 seeds germinate?

A.About 2.5%B.About 0.15%C.About 2.3%D.About 16%

Question 14

A student claims that because $P (A) = 0.5$ and $P (B) = 0.4$ , events $A$ and $B$ cannot both occur since $P (A) + P (B) = 0.9 < 1$ . Is this reasoning valid?

A.Yes; if

P (A) + P (B) < 1

, they must be mutually exclusive.B.No;

P (A) + P (B) < 1

does not prevent both events from occurring simultaneously.C.Yes; the sum of individual probabilities must equal 1 for events to overlap.D.No; events can co-occur only if

P (A) + P (B) > 1

Question 15

The regression of $ln (y)$ on $x$ produces a better fit than the regression of $y$ on $x$ . What does this suggest about the relationship between $x$ and $y$ ?

A.The relationship between

x

and

y

is exponential.B.The relationship between

x

and

y

is linear.C.The relationship between

x

and

y

is a power function.D.

x

must be transformed, not

y

AP Statistics Medium practice — Free with Answer Explanations | Test Practice Hub