Question 1

Which of the following best describes the Central Limit Theorem (CLT)?

Accepted Answer

The CLT states that, for a sufficiently large sample size, the distribution of the sample means approaches a normal distribution, regardless of the population's distribution.

Question 2

A researcher wants to estimate the average height of all students at a university. Which of the following sampling methods is most likely to produce a representative sample?

Accepted Answer

Randomly selecting 100 students from the university's enrollment list.

Question 3

Which formula correctly calculates the sample variance $$s^2$$ for a data set with $$n$$ observations and sample mean $$\overline{x}$$?

Accepted Answer

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

Question 4

A pharmaceutical company tests a new drug and finds that 8 out of 100 patients experience side effects. What is the sample proportion $$\hat{p} of $$patients with side effects?

Accepted Answer

$$\hat{p} = 0.08$$

Question 5

Which of the following is NOT a requirement for using the normal approximation to the binomial distribution?

Accepted Answer

The probability of success $$p is $$close to 0 or 1.

Question 6

A histogram is used to:

Accepted Answer

Display the frequency distribution of quantitative data.

Question 7

Which of the following is the correct formula for a confidence interval for a population mean $$\mu$$ when the population standard deviation $$\sigma is $$unknown and the sample size is small?

Accepted Answer

$$\overline{x} \pm t^* \frac{s}{\sqrt{n}}$$

Question 8

Suppose you roll a fair six-sided die. What is the probability of rolling a number greater than 4?

Accepted Answer

$$\frac{1}{3}$$

Question 9

Which of the following statements about correlation is TRUE?

Accepted Answer

A correlation coefficient of $$r = 1$$ means there is a perfect positive linear relationship.

Question 10

A boxplot is useful for:

Accepted Answer

Identifying outliers and visualizing the spread of quantitative data.

Question 11

A researcher wants to test if a new teaching method improves test scores. Which is the correct null hypothesis $$H_0$$ for a two-tailed test?

Accepted Answer

$$H_0$$: \mu = \$$mu_0$$

Question 12

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 13

If the probability of rain tomorrow is 0.3, what is the probability that it will NOT rain?

Accepted Answer

$$0.7$$

Question 14

Which of the following is a correct interpretation of a 95% confidence interval for a population mean?

Accepted Answer

If we took many samples, about 95% of the calculated intervals would contain the population mean.

Question 15

Which of the following is the correct formula for the slope $$b_1 in $$simple linear regression?

Accepted Answer

$$b_1$$ = \frac{\sum (x_i - \overline{x})(y_i - \overline{y})}{\sum (x_i - \overline{x}$$)^2$$}$$

Question 16

A chi-square test for independence is used to:

Accepted Answer

Test if two categorical variables are related.

Question 17

Which of the following is a measure of relative standing?

Accepted Answer

Z-score

Question 18

A student calculates a $$z-$$score of $$-2.5$$ for their exam score. What does this indicate?

Accepted Answer

The student's score is 2.5 standard deviations below the mean.

Question 19

Which of the following is an example of a Type I error in hypothesis testing?

Accepted Answer

Rejecting a true null hypothesis.

STA 2023 Elementary Statistics – Syllabus and Course Structure Study Guide

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