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AP Statistics Easy practice

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Question 1

A researcher collects a random sample of 20 measurements and wants to construct a confidence interval for the population mean. The population standard deviation is unknown. Which distribution should be used?

A.Standard normal (

z

) distributionB.

t

-distribution with 20 degrees of freedomC.

t

-distribution with 19 degrees of freedomD.

χ^{2}

distribution with 19 degrees of freedom

Question 2

A discrete random variable $X$ has the probability distribution shown. What is $E (X)$ ?

$x$	1	2	3	4
$P (X = x)$	0.10	0.30	0.40	0.20

A.2.50B.2.70C.3.00D.1.00

Question 3

A candy machine has a 30% chance of dispensing a rare flavor. You try the machine 10 times. Using the binomial model, what is the probability of getting the rare flavor at least once?

1 - (0.30)^{10}

10 \times 0.30 = 0.30

1 - (0.70)^{10} \approx 0.972

(0.30)^{1} (0.70)^{9} \approx 0.121

Question 4

A researcher wants to estimate a population proportion to within ±0.04 with 95% confidence, but has no prior estimate of $p$ . What minimum sample size is needed?

A.385B.601C.25D.2401

Question 5

A stemplot of hourly wages (in dollars) for 10 part-time workers is shown below. What is the median wage?

Stem	Leaves
8	2 5
9	1 3 7
10	0 4 4 8
11	2 6

A.$9.70B.$10.00C.$10.02D.$9.85

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Question 6

In a goodness-of-fit test, the expected frequency for one category is $E = 2.5$ . Should the chi-square test proceed?

A.Yes; as long as

n > 30

, expected frequencies do not matter.B.No; the expected frequency condition requires all expected counts to be at least 5.C.Yes; as long as the observed frequency for that category is at least 5.D.No; chi-square tests require expected counts of at least 10.

Question 7

The regression equation for predicting a city's high temperature in July ( $y$ , °F) from its latitude ( $x$ , degrees north) is $\overset{y}{^} = 115 - 1.1 x$ . Interpret the $y$ -intercept in context.

A.At 0° latitude (equator), the predicted July high is 115°F.B.For each degree increase in latitude, temperature decreases by 115°F.C.The average July high temperature across all cities is 115°F.D.The

y

-intercept has no meaningful interpretation because latitude cannot equal zero.

Question 8

For the test $H_{0} : p = 0.80$ vs. $H_{a} : p < 0.80$ using the data from the previous question ( $n = 100$ , $\overset{p}{^} = 0.72$ ), the $z$ -test statistic is approximately $- 2.0$ and the $p$ -value is 0.023. At $α = 0.05$ , what is the correct conclusion?

A.Fail to reject

H_{0}

; there is insufficient evidence that fewer than 80% of customers are satisfied.B.Reject

H_{0}

; there is convincing evidence that fewer than 80% of customers are satisfied.C.Reject

H_{0}

; we have proved the true satisfaction rate is exactly 0.72.D.Accept

H_{0}

; the satisfaction rate is 80%.

Question 9

A regression of salary ( $y$ , thousands of dollars) on years of experience ( $x$ ) yields $r^{2} = 0.64$ . Which interpretation is correct?

r = 0.64

, indicating a moderately positive linear association.B.64% of the variation in salary is explained by the linear relationship with years of experience.C.64% of employees have salaries predicted correctly by the model.D.Years of experience causes 64% of the increase in salary.

Question 10

A random sample of 16 light bulbs had a mean life of $\overset{x}{ˉ} = 1, 200$ hours with $s = 80$ hours. Construct a 95% confidence interval for the true mean life. (Use $t^{*} \approx 2.131$ for $df = 15$ .)

(1, 143, 1, 257)

(1, 157.4, 1, 242.6)

(1, 040, 1, 360)

(1, 182.6, 1, 217.4)

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Question 11

A researcher conducts a one-sample $t$ -test with $n = 12$ , $\overset{x}{ˉ} = 55$ , $s = 8$ , testing $H_{0} : μ = 50$ vs. $H_{a} : μ \neq = 50$ . Compute the $t$ test statistic.

t = 0.625

t \approx 2.17

t \approx 1.73

t = 5.0

Question 12

A chi-square test of independence produces $χ^{2} = 9.2$ with $df = 3$ . The critical value at $α = 0.05$ is 7.815. What is the correct conclusion?

A.Fail to reject

H_{0}

; the variables are independent.B.Reject

H_{0}

; there is convincing evidence of an association between the two variables.C.Reject

H_{0}

; we have proven the variables are dependent.D.The test is inconclusive because

χ^{2} \approx 9

is not far above the critical value.

Question 13

Events $A$ and $B$ are mutually exclusive with $P (A) = 0.30$ and $P (B) = 0.45$ . What is $P (A or B)$ ?

A.0.135B.0.75C.0.775D.1.00

Question 14

A regression output for predicting salary from years of experience shows: slope $b = 3.2$ , $S E_{b} = 0.8$ . What is the $t$ statistic for testing $H_{0} : β = 0$ ?

t = 0.25

t = 4.0

t = 2.56

t = 3.2

Question 15

Two independent random variables $X$ and $Y$ have means $μ_{X} = 10$ , $μ_{Y} = 6$ , and standard deviations $σ_{X} = 3$ , $σ_{Y} = 4$ . What are the mean and standard deviation of $X + Y$ ?

μ = 16

σ = 7

μ = 16

σ = 5

μ = 4

σ = 5

μ = 16

σ = 25

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