Question 1

Which of the following best describes the difference between a population and a sample in statistics?

Accepted Answer

A population includes all individuals or items of interest, while a sample is a subset selected from the population.

Question 2

A pharmaceutical company wants to estimate the average recovery time for a new medication. They collect data from 200 randomly selected patients who used the medication. Which term best describes the 200 patients?

Accepted Answer

Sample

Question 3

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

Accepted Answer

Standard deviation

Question 4

A researcher summarizes the heights of 1,000 students using a histogram. What type of data visualization is this?

Accepted Answer

A graphical summary of quantitative data

Question 5

If a data set is skewed to the right, which of the following is most likely true?

Accepted Answer

The mean is greater than the median.

Question 6

A z-score is calculated using which of the following formulas?

Accepted Answer

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

Question 7

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

Accepted Answer

As the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the population's distribution.

Question 8

A hospital administrator wants to know if there is a relationship between hours of sleep and number of errors made by nurses during a shift. Which statistical method is most appropriate?

Accepted Answer

Correlation and regression analysis

Question 9

Which of the following is the correct formula for the sample variance $$s^2$$?

Accepted Answer

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

Question 10

A study finds a correlation coefficient $$r = -0.85$$ between hours spent watching TV and GPA among college students. Which of the following best describes this relationship?

Accepted Answer

A strong negative linear relationship

Question 11

Which of the following is a valid probability value?

Accepted Answer

$$0.25$$

Question 12

A fair six-sided die is rolled. What is the probability of rolling a number greater than 4?

Accepted Answer

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

Question 13

Which of the following best describes a random variable?

Accepted Answer

A variable whose value is determined by the outcome of a random experiment

Question 14

A normal distribution has mean $$\mu = 100$$ and standard deviation $$\sigma = 15. $$What is the z-score for a value of $$x = 130$$?

Accepted Answer

$$z = 2$$

Question 15

Which of the following is NOT an assumption of the binomial model?

Accepted Answer

The probability of success changes from trial to trial.

Question 16

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 true population mean lies between 50 and 60.

Question 17

A researcher wants to test if a new teaching method improves test scores. Which of the following is the correct null hypothesis $$H_0$$?

Accepted Answer

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

Question 18

Which of the following best describes a Type I error in hypothesis testing?

Accepted Answer

Rejecting the null hypothesis when it is actually true

Question 19

A medical researcher is comparing the effectiveness of two drugs. Which statistical test is most appropriate for comparing the means of two independent groups?

Accepted Answer

Two-sample t-test

Question 20

A survey is conducted to estimate the proportion of voters who support a new policy. Which formula is used to calculate the standard error of the sample proportion $$\hat{p}$$?

Accepted Answer

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

Statistics I (MATH 1200) Syllabus Study Guide

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