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

$$P(A \text{ and } B) = P(A) \times P(B)$$

Question 1

Which of the following best describes the purpose of descriptive statistics in a medical research study investigating the effects of a new drug?

Accepted Answer

To summarize and present the collected data, such as mean blood pressure and standard deviation.

Question 2

A researcher wants to estimate the average height of adult males in a city. She randomly selects 100 men and calculates their mean height. Which statistical concept is illustrated by this scenario?

Accepted Answer

Sample statistic

Question 3

Which of the following is the correct formula for the sample variance $$s^2$$ given a sample of $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

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

Question 4

A hospital records the number of patients admitted each day for a month. Which type of data is this?

Accepted Answer

Discrete quantitative

Question 5

In a study, the variable 'temperature' is measured in degrees Celsius. Which level of measurement does this represent?

Accepted Answer

Interval

Question 6

A researcher is investigating whether a new teaching method improves test scores. She randomly assigns students to two groups: one uses the new method, the other uses the traditional method. Which type of study is this?

Accepted Answer

Experimental study

Question 7

Which of the following best describes a stratified sampling method in a survey of university students?

Accepted Answer

Dividing students into majors and randomly sampling from each major.

Question 8

If the mean of a data set is 50 and the standard deviation is 5, what is the z-score for a value of 60?

Accepted Answer

$$z = \frac{60 - 50}{5} = 2$$

Question 9

A pharmaceutical company wants to know if a new drug is more effective than the current standard. They conduct a hypothesis test and obtain a p-value of 0.03. If their significance level is 0.05, what should they conclude?

Accepted Answer

Reject the null hypothesis; the drug is more effective.

Question 10

Which formula correctly represents the confidence interval for the population mean $$\mu$$ when the population standard deviation $$\sigma is $$known?

Accepted Answer

$$\bar{x} \pm z^* \frac{\sigma}{\sqrt{n}}$$

Question 11

A student wants to determine if there is a relationship between hours studied and exam scores. Which statistical method should she use?

Accepted Answer

Correlation analysis

Question 12

Which of the following is an example of a lurking variable in a study examining the relationship between exercise and weight loss?

Accepted Answer

Diet

Question 13

A researcher collects data on the number of hours students sleep and their GPA. She finds a correlation coefficient $$r = 0.8. $$What does this indicate?

Accepted Answer

There is a strong positive linear relationship between hours slept and GPA.

Question 14

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

Accepted Answer

$$P(A 	ext{ and } B) = P(A) 	imes P(B)$$

Question 15

A quality control manager inspects 10 light bulbs and finds 2 defective. What is the probability that the next bulb inspected is defective, assuming the bulbs are randomly selected from a large batch?

Accepted Answer

Cannot be determined from the sample; need population information.

Question 16

Which formula represents the expected value $$E(X) of a $$discrete random variable $$X$$ with possible values $$x_1$$, $$x_2$$, ..., x_n$$ and probabilities p_1$, p_2$, ..., p_n$$?

Accepted Answer

$$E(X) = \sum_{i=1}^{n} x_i \cdot p_i$$

Question 17

A researcher wants to test if the mean cholesterol level in a population is different from 200 mg/dL. Which hypothesis test should she use?

Accepted Answer

One-sample t-test

Question 18

Which formula is used to calculate the margin of error for a proportion in a confidence interval?

Accepted Answer

$$z^* \sqrt{\frac{p(1-p)}{n}}$$

Question 19

A study finds that students who eat breakfast score higher on tests. Which of the following best explains why causation cannot be concluded from this result?

Accepted Answer

There may be confounding variables, such as socioeconomic status.

MTH 155 Statistical Reasoning: Course Structure and Chapter Overview

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