Question 1

Which of the following best describes the difference between a parameter and a statistic?

Accepted Answer

A parameter is a numerical summary of a population, while a statistic is a numerical summary of a sample.

Question 2

A pharmaceutical company wants to estimate the average recovery time for a new medication. They randomly select 100 patients from a list of all patients who used the medication. Which sampling method is being used?

Accepted Answer

Simple random sampling

Question 3

Which of the following is an example of a qualitative (categorical) variable?

Accepted Answer

Blood type (A, B, AB, O)

Question 4

Suppose the heights of adult men in a city are normally distributed with mean $$\mu = 70$$ inches and standard deviation $$\sigma = 3$$ inches. What is the probability that a randomly selected man is taller than 76 inches? (Use the standard normal distribution.)

Accepted Answer

$$P(Z \u003e 2) \approx 0.0228$$

Question 5

A researcher wants to test whether a new teaching method improves test scores. The null hypothesis is $$H_0$$: \mu = 75$$ and the alternative is H_a$$: \mu \u003e 75$$. If the sample mean is 78, the sample standard deviation is 6, and the sample size is 36, what is the value of the test statistic?

Accepted Answer

$$z = \frac{78 - 75}{6/\sqrt{36}} = 3$$

Question 6

Which of the following statements about the binomial distribution is TRUE?

Accepted Answer

Each trial is independent and has only two possible outcomes.

Question 7

A fair coin is flipped 5 times. What is the probability of getting exactly 3 heads? (Use the binomial formula.)

Accepted Answer

$$P(X=3) = \binom{5}{3} (0.5)^3$ (0.5)^2$ = 0.3125$$

Question 8

Which of the following is NOT an ethical issue in statistics?

Accepted Answer

Randomly sampling from the population

Question 9

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 lies between 50 and 60.

Question 10

Which of the following is the formula for the correlation coefficient $$r$$ between two variables $$X$$ and $$Y$$?

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 11

A hospital administrator wants to know if there is a relationship between hours of nurse staffing and patient recovery rates. Which statistical method should be used to analyze this relationship?

Accepted Answer

Linear regression

Question 12

If the probability of event $$A is$$ $$0.4$$ and the probability of event $$B is$$ $$0.5$$, and $$A$$ and $$B$$ are mutually exclusive, what is $$P(A \cup B)$$?

Accepted Answer

$$P(A \cup B) = 0.4 + 0.5 = 0.9$$

Question 13

Which of the following is a sign that statistics are being presented in a misleading manner?

Accepted Answer

A graph with a truncated y-axis exaggerating differences

Question 14

A study finds a strong positive correlation between ice cream sales and drowning incidents. Which of the following is the best explanation for this finding?

Accepted Answer

There is a lurking variable, such as temperature, that affects both variables.

Question 15

A sample of 25 students has a mean test score of 80 and a standard deviation of 10. What is the standard error of the mean?

Accepted Answer

$$	ext{SE} = \frac{10}{\sqrt{25}} = 2$$

Question 16

Which of the following is the correct formula for a 95% confidence interval for a population mean when the population standard deviation $$\sigma is $$known?

Accepted Answer

$$\bar{x} \pm z_{0.025} \frac{\sigma}{\sqrt{n}}$$

Question 17

A company claims that their batteries last an average of 100 hours. A consumer group tests 50 batteries and finds a sample mean of 98 hours with a known population standard deviation of 5 hours. What is the value of the $$z-$$statistic for testing the company's claim?

Accepted Answer

$$z = \frac{98 - 100}{5/\sqrt{50}} = -2.83$$

Question 18

Which of the following is an example of conditional probability?

Accepted Answer

The probability that a patient has disease A given that they tested positive.

Question 19

A regression analysis yields the equation $$\hat{y} = 2 + 3x. $$What is the predicted value of $$y$$ when $$x = 4$$?

Accepted Answer

$$\hat{y} = 2 + 3 	imes 4 = 14$$

Question 20

Which of the following best describes the purpose of hypothesis testing in statistics?

Accepted Answer

To make inferences about a population based on sample data.

MAT 124 Statistics: Course Syllabus and Overview

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