Q: Which formula is used to calculate the probability of two independent events $$A$$ and $$B$$ both occurring?

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

Question 1

Which of the following best describes a simple random sample?

Accepted Answer

A sample where every individual has an equal chance of being selected, and every possible sample of the same size has an equal chance of being chosen.

Question 2

A researcher wants to study the effect of a new drug on blood pressure. She randomly assigns participants to either the drug group or the placebo group. Which sampling method is she using?

Accepted Answer

Random assignment (experimental design)

Question 3

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

Accepted Answer

Selecting participants who are easiest to reach

Question 4

Given the following data set: 2, 4, 4, 6, 8. What is the mean?

Accepted Answer

Mean $$= \frac{2+4+4+6+8}{5} = \frac{24}{5} = 4.8$$

Question 5

Which measure of central tendency is most appropriate when a data set contains extreme outliers?

Accepted Answer

Median

Question 6

A frequency distribution is used to:

Accepted Answer

Organize raw data into classes or intervals and show the number of observations in each class.

Question 7

If the standard deviation of a data set is large, what does this indicate about the data?

Accepted Answer

The data values are spread out widely from the mean.

Question 8

Which formula is used to calculate the variance of a sample?

Accepted Answer

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

Question 9

A scatter plot is useful for:

Accepted Answer

Visualizing the relationship between two quantitative variables.

Question 10

Which equation represents the least-squares regression line?

Accepted Answer

Regression line $$y = a + bx$$

Question 11

If a correlation coefficient $$r is $$close to $$-1$$, what does this indicate?

Accepted Answer

There is a strong negative linear relationship between the two variables.

Question 12

Which formula is used to calculate the probability of two independent events $$A$$ and $$B$$ both occurring?

Accepted Answer

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

Question 13

A binomial probability distribution is appropriate when:

Accepted Answer

Each trial has two possible outcomes, trials are independent, and the probability of success is constant.

Question 14

Which formula is used to calculate the probability of exactly $$k$$ successes in $$n$$ binomial trials?

Accepted Answer

$$P(X = k) = \binom{n}{k} p^k (1-p$$)^{n-k}$$

Question 15

The normal probability density function is given by:

Accepted Answer

$$f(x) = \frac{1}{\sigma \sqrt{2\pi}} e$$^{-\frac{(x-\mu)^2}$${2\$$sigma^2$$}}$$

Question 16

A sample of 100 students has a mean height of 170 cm and a standard deviation of 10 cm. What is the $$z-$$score for a student who is 190 cm tall?

Accepted Answer

$$z = \frac{190 - 170}{10} = 2$$

Question 17

Which statement best explains why the distribution of sample means is often approximately normal, even if the parent population is not normal?

Accepted Answer

The Central Limit Theorem states that as sample size increases, the distribution of sample means approaches normality.

Question 18

A 95% confidence interval for a population mean is calculated as $$\bar{x} \pm z^* \frac{\sigma}{\sqrt{n}}. $$What does the value $$z^*$$ represent?

Accepted Answer

The critical value from the standard normal distribution corresponding to the desired confidence level.

Question 19

In hypothesis testing, what is the null hypothesis ($$H_0$$)?

Accepted Answer

A statement that there is no effect or no difference, and it is tested directly.

Question 20

When comparing two population means using independent samples, which formula is used for the test statistic?

Accepted Answer

$$t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1$^2}{n_1$} + \frac{s_2$^2}{n_2$}}}$$

CGS MA 113 – Elementary Statistics: Syllabus and Weekly Topics Study Guide

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