Question 1

Which of the following best describes the difference between descriptive and inferential statistics?

Accepted Answer

Descriptive statistics summarize and organize data, while inferential statistics use sample data to make generalizations about a population.

Question 2

A researcher wants to study the effect of a new medication on blood pressure. She randomly assigns 100 patients to receive either the medication or a placebo. Which type of study design is this?

Accepted Answer

Experimental study

Question 3

Which of the following is a correct formula for the sample mean $$\bar{x} of$$ $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$

Question 4

A frequency distribution is used to:

Accepted Answer

Summarize data by showing the number of observations in each category or interval.

Question 5

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

Accepted Answer

Range

Question 6

If the probability of event $$A is$$ $$P(A) = 0.3$$ and the probability of event $$B is$$ $$P(B) = 0.5$$, and $$A$$ and $$B$$ are independent, what is the probability that both $$A$$ and $$B$$ occur?

Accepted Answer

$$P(A \cap B) = 0.15$$

Question 7

Which formula represents the standard deviation $$s of a $$sample of $$n$$ values $$x_1$$, $$x_2$$, ..., x_n$$ with mean $$\bar{x}$$?

Accepted Answer

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

Question 8

A normal distribution is characterized by which of the following properties?

Accepted Answer

It is symmetric and bell-shaped.

Question 9

Suppose the heights of adult men are normally distributed with mean $$\mu = 70$$ inches and standard deviation $$\sigma = 3$$ inches. What is the $$z-$$score for a man who is 76 inches tall?

Accepted Answer

$$z = \frac{76 - 70}{3} = 2$$

Question 10

Which of the following statements about the Central Limit Theorem is TRUE?

Accepted Answer

The sampling distribution of the sample mean will be approximately normal if the sample size is large enough, regardless of the population distribution.

Question 11

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

Accepted Answer

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

Question 12

Which of the following is the correct null hypothesis for testing whether the mean weight of a population is 150 pounds?

Accepted Answer

$$H_0$$: \mu = 150$$

Question 13

A researcher conducts a hypothesis test and obtains a $$p-$$value of 0.03. If the significance level is $$\alpha = 0.05$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis.

Question 14

Which formula is used to calculate the correlation coefficient $$r$$ for paired data $$(x_1$, y_1$), ..., (x_n, y_n)$$?

Accepted Answer

$$r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2$ \sum (y_i - \bar{y})^2$}}$$

Question 15

Which of the following best describes the purpose of linear regression analysis?

Accepted Answer

To predict the value of one variable based on the value of another variable.

Question 16

A binomial experiment has $$n = 10$$ trials and probability of success $$p = 0.4. $$What is the probability of exactly 3 successes? (Use the binomial probability formula.)

Accepted Answer

$$P(X = 3) = \binom{10}{3} (0.4)^3$ (0.6)^7$

Question 17

Which of the following is an example of a parameter, not a statistic?

Accepted Answer

The proportion of all voters in a city who support a candidate.

Question 18

If a 90% confidence interval for a population proportion is $$(0.45, 0.55)$$, what happens to the width of the interval if the confidence level is increased to 95%?

Accepted Answer

The interval becomes wider.

Question 19

Which of the following is a correct application of the addition rule for probability?

Accepted Answer

For any two events $$A$$ and $$B$$, $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$

STA 2023 Statistical Methods – Course Syllabus and Study Guide

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