Question 1

A pharmaceutical company tests a new drug and finds a 95% confidence interval for the difference in mean recovery times between the new drug and the standard drug to be $$(-2.1, 0.5)$$ days. What does this confidence interval suggest about the difference in population means?

Accepted Answer

There is no significant difference in mean recovery times between the two drugs at the 95% confidence level.

Question 2

Which of the following is NOT part of the 5-number summary for a data set?

Accepted Answer

Mean

Question 3

Given the data set: $$3, 7, 7, 19, 21, 23, 23, 23, 30$$, what is the median?

Accepted Answer

$$21$$

Question 4

A sample of 100 people is surveyed, and 40 say they prefer tea over coffee. What is the empirical probability that a randomly selected person from this sample prefers tea?

Accepted Answer

$$0.40$$

Question 5

Which of the following best defines a parameter?

Accepted Answer

A numerical measurement describing a characteristic of a population.

Question 6

Given a grouped frequency distribution table with class limits 10-19, 20-29, 30-39, what is the class width?

Accepted Answer

$$10$$

Question 7

Which of the following is a correct symbolic representation for testing the claim that the mean weight $$ar{x} of $$apples is less than 150g?

Accepted Answer

$$H_0$$: \mu = 150$$, H_a$$: \mu \u003c 150$$

Question 8

A data value is 2.5 standard deviations above the mean. What is its $$z-$$score, and is it considered significant at the 5% level (two-tailed)?

Accepted Answer

$$z = 2.5$$, which is significant at the 5\% level.

Question 9

Which of the following is a Type I error?

Accepted Answer

Rejecting the null hypothesis when it is actually true.

Question 10

A researcher wants to know if a new teaching method improves test scores. Which type of hypothesis test should be conducted?

Accepted Answer

A two-sample $$t-$$test for means.

Question 11

Which of the following statements about the correlation coefficient $$r is $$true?

Accepted Answer

$$r$$ measures the strength and direction of a linear relationship between two quantitative variables.

Question 12

A data set of home prices contains several extremely high values. Which measure of central tendency is most affected by these outliers?

Accepted Answer

Mean

Question 13

Which of the following best describes a sampling distribution?

Accepted Answer

The probability distribution of a statistic based on all possible samples of a specific size from a population.

Question 14

A fair coin is tossed 5 times. What is the probability of getting exactly 3 heads? (Use the binomial formula: $$P(X = k) = \binom{n}{k} p^k (1-p$$)^{n-k}$$)

Accepted Answer

$$0.3125$$

Question 15

Which of the following is a correct definition of a random variable?

Accepted Answer

A variable whose value is a numerical outcome of a random phenomenon.

Question 16

A sample has a variance of $$16. $$What is the standard deviation?

Accepted Answer

$$4$$

Question 17

Which of the following is an example of cluster sampling?

Accepted Answer

Randomly selecting 5 classrooms from a school and surveying all students in those classrooms.

Question 18

If the null hypothesis is rejected in a hypothesis test, what is the correct nontechnical conclusion?

Accepted Answer

There is sufficient evidence to support the alternative claim.

Question 19

Which of the following is a correct definition of a mutually exclusive event?

Accepted Answer

Two events that cannot occur at the same time.

Question 20

A point at coordinates $$(8, 2) on a $$scatterplot is far from the other points and greatly affects the regression line. How should this point be classified?

Accepted Answer

Both an outlier and an influential point.

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