Q: A pharmaceutical company wants to test whether a new drug lowers blood pressure more effectively than the current standard. Which of the following is the most appropriate null hypothesis ($$H_0) $$for this scenario?

$$H_0$$: \text{There is no difference in effectiveness between the new drug and the standard}$$

Q: A sample of 50 Berry College students has a mean GPA of $$3.2$$ with a standard deviation of $$0.4. $$What is the $$95\%$$ confidence interval for the mean GPA? (Use $$z^* = 1.96$$ for $$95\%$$ confidence.)

$$3.2 \pm 1.96 \times \dfrac{0.4}{\sqrt{50}}$$

Question 1

Which of the following best describes the difference between descriptive and inferential statistics?

Accepted Answer

Descriptive statistics summarize and organize data, while inferential statistics use probability to make predictions or draw conclusions about a population based on a sample.

Question 2

A pharmaceutical company wants to test whether a new drug lowers blood pressure more effectively than the current standard. Which of the following is the most appropriate null hypothesis ($$H_0) $$for this scenario?

Accepted Answer

$$H_0$$: 	ext{There is no difference in effectiveness between the new drug and the standard}$$

Question 3

Suppose the heights (in cm) of a group of college students are normally distributed with a mean $$\mu = 170$$ and a standard deviation $$\sigma = 10. $$What is the $$z-$$score for a student who is 185 cm tall?

Accepted Answer

$$z = \dfrac{185 - 170}{10} = 1.5$$

Question 4

A researcher collects data on the number of hours students study per week and their exam scores. Which statistical method is most appropriate to analyze the relationship between these two variables?

Accepted Answer

Simple linear regression

Question 5

If the probability of rain on any given day in April is $$0.3$$, what is the probability that it will NOT rain on a randomly selected day in April?

Accepted Answer

$$0.7$$

Question 6

A sample of 50 Berry College students has a mean GPA of $$3.2$$ with a standard deviation of $$0.4. $$What is the $$95\%$$ confidence interval for the mean GPA? (Use $$z^* = 1.96$$ for $$95\%$$ confidence.)

Accepted Answer

$$3.2 \pm 1.96 	imes \dfrac{0.4}{\sqrt{50}}$$

Question 7

Which of the following is a correct interpretation of a $$p-$$value in hypothesis testing?

Accepted Answer

The probability of obtaining a result as extreme or more extreme than the observed result, assuming the null hypothesis is true.

Question 8

A hospital administrator wants to estimate the average wait time in the emergency room. Which sampling method would best ensure that all shifts (morning, afternoon, night) are represented proportionally in the sample?

Accepted Answer

Stratified random sampling

Question 9

Which of the following statements about the correlation coefficient $$r is $$TRUE?

Accepted Answer

$$r$$ measures the strength and direction of a linear relationship between two quantitative variables.

Question 10

A fair six-sided die is rolled twice. What is the probability of rolling a $$6 on $$both rolls?

Accepted Answer

$$\dfrac{1}{36}$$

Question 11

A data set has a mean of $$50$$ and a standard deviation of $$5. If a $$value in the data set is $$60$$, what is its $$z-$$score?

Accepted Answer

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

Question 12

Which of the following is NOT an assumption of simple linear regression?

Accepted Answer

The independent variable is categorical.

Question 13

A researcher wants to test if a coin is fair. She flips it $$100$$ times and gets $$60$$ heads. Which statistical test should she use?

Accepted Answer

One-sample proportion $$z-$$test

Question 14

Which of the following best describes the Central Limit Theorem?

Accepted Answer

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

Question 15

A student calculates a $$90\%$$ confidence interval for the average number of hours students sleep per night and gets $$(6.5, 7.5). $$Which of the following is a correct interpretation?

Accepted Answer

We are $$90\%$$ confident that the true mean number of hours students sleep per night is between $$6.5$$ and $$7.5.$$

Question 16

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 17

A researcher is testing the effect of a new fertilizer on plant growth. She randomly assigns 30 plants to receive the new fertilizer and 30 plants to receive the standard fertilizer. Which type of study design is this?

Accepted Answer

Experimental study

Question 18

If two events $$A$$ and $$B$$ are independent, which of the following is true?

Accepted Answer

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

Question 19

A company claims that their batteries last an average of $$100$$ hours. A consumer group tests $$25$$ batteries and finds a sample mean of $$98$$ hours with a standard deviation of $$4$$ hours. What is the test statistic for a one-sample $$t-$$test?

Accepted Answer

$$t = \dfrac{98 - 100}{4/\sqrt{25}} = -2.5$$

MAT111F Elementary Statistics – Syllabus and Course Structure Overview

Guida di studio - Domande di pratica

Study guide - Flashcard