Q: If two events $$A$$ and $$B$$ are independent, which equation must be true?

$$P(A \cap B) = P(A) \times P(B)$$

Question 1

Which of the following best describes the purpose of descriptive statistics in a research study?

Accepted Answer

To organize and summarize data so that patterns can be easily interpreted.

Question 2

A pharmaceutical company wants to estimate the average recovery time for a new medication. They randomly select 100 patients and calculate the mean recovery time. Which statistical concept is being applied?

Accepted Answer

Sampling distribution of the mean

Question 3

Which of the following is NOT a measure of central tendency?

Accepted Answer

Standard deviation

Question 4

A researcher claims that the average commute time in a city is 30 minutes. You collect a sample and perform a hypothesis test. If your p-value is $$0.03$$ and your significance level is $$0.05$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis; there is enough evidence to suggest the average commute time is not 30 minutes.

Question 5

Which formula correctly calculates the variance $$s^2 of a $$sample with $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$ and sample mean $$\overline{x}$$?

Accepted Answer

$$s^2$$ = \frac{\sum_{i=1}^n (x_i - \overline{x}$$)^2$$}{n-1}$$

Question 6

A boxplot is used to display which of the following?

Accepted Answer

The five-number summary of a quantitative variable

Question 7

If two events $$A$$ and $$B$$ are independent, which equation must be true?

Accepted Answer

$$P(A \cap B) = P(A) 	imes P(B)$$

Question 8

A fair die is rolled twice. What is the probability of rolling a 6 on both rolls?

Accepted Answer

$$\frac{1}{36}$$

Question 9

Which of the following statements about the normal distribution is FALSE?

Accepted Answer

It is skewed to the right.

Question 10

A 95% confidence interval for a population mean is calculated as $$(50, 60). $$Which interpretation is correct?

Accepted Answer

We are 95% confident that the population mean is between 50 and 60.

Question 11

Which of the following is an example of a discrete random variable?

Accepted Answer

The number of cars passing through an intersection in an hour

Question 12

A hospital administrator wants to know if a new policy has changed the average patient wait time. Which statistical method should be used?

Accepted Answer

Conducting a hypothesis test for the population mean

Question 13

Which of the following best describes the p-value in hypothesis testing?

Accepted Answer

The probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis.

Question 14

Which formula is used to calculate the z-score for a value $$x$$ from a population with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

$$z = \frac{x - \mu}{\sigma}$$

Question 15

A study finds that 20% of a population is left-handed. If 10 people are randomly selected, what is the expected number of left-handed people?

Accepted Answer

2

Question 16

Which of the following is a potential source of bias in sampling?

Accepted Answer

Selecting participants who volunteer for the study

Question 17

Which rule is used to find the probability of either event $$A or $$event $$B$$ occurring (for any two events)?

Accepted Answer

$$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$

Question 18

A researcher wants to estimate the proportion of voters who support a new law. Which formula should be used to calculate the standard error of the sample proportion $$\hat{p}$$ for a sample of size $$n$$?

Accepted Answer

$$SE = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

Question 19

Which of the following is NOT part of the five-number summary?

Accepted Answer

Mean

Question 20

A contingency table is most useful for analyzing which type of data?

Accepted Answer

The relationship between two categorical variables

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