Question 1

Which of the following best describes the purpose of descriptive statistics in a medical research study investigating the average blood pressure of adults in a city?

Accepted Answer

To summarize and present the main features of the collected blood pressure data.

Question 2

A pharmaceutical company wants to test if a new drug lowers cholesterol more effectively than the current standard. Which statistical method should they use to compare the mean cholesterol levels between two independent groups?

Accepted Answer

Independent samples t-test

Question 3

Suppose a researcher collects the following sample data on the number of hours students study per week: 5, 7, 8, 10, 10, 12, 15. What is the median number of study hours?

Accepted Answer

$$10$$

Question 4

A hospital administrator wants to estimate the proportion of patients who recover within 3 days after surgery. Which formula should be used to construct a 95% confidence interval for the population proportion $$p$$?

Accepted Answer

$$\hat{p} \pm z^* \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$$

Question 5

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

Accepted Answer

It states that the distribution of sample means approaches a normal distribution as sample size increases, regardless of the population's distribution.

Question 6

A scientist is testing whether a coin is fair. She flips the coin 100 times and gets 60 heads. Which hypothesis test should she use?

Accepted Answer

Test for a population proportion

Question 7

A teacher wants to know if students in her class score differently on two exams. She records each student's scores on both exams. Which statistical test is most appropriate?

Accepted Answer

Paired t-test

Question 8

A researcher finds a correlation coefficient $$r = 0.85$$ between hours studied and exam scores. What does this indicate?

Accepted Answer

There is a strong positive linear relationship between hours studied and exam scores.

Question 9

A biologist wants to compare the mean heights of three different plant species grown under identical conditions. Which statistical method should she use?

Accepted Answer

One-way ANOVA

Question 10

A company claims that their batteries last an average of 100 hours. A consumer group tests 30 batteries and finds a sample mean of 95 hours with a standard deviation of 10 hours. Which formula should be used to calculate the 95% confidence interval for the mean battery life?

Accepted Answer

$$\bar{x} \pm t^* \dfrac{s}{\sqrt{n}}$$

Question 11

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

Accepted Answer

The probability of observing data as extreme as the sample, assuming the null hypothesis is true.

Question 12

A researcher wants to test if the variance in exam scores differs between two classes. Which statistical test should be used?

Accepted Answer

F-test for equality of variances

Question 13

A study finds that the distribution of household incomes in a city is highly skewed to the right. Which measure of central tendency is most likely to be greater than the others?

Accepted Answer

Mean

Question 14

A scientist wants to predict the weight of a fish based on its length using a linear model. Which equation represents the regression line?

Accepted Answer

$$\hat{y} = a + bx$$

Question 15

A researcher is testing the effectiveness of a new vaccine. She randomly assigns participants to receive either the vaccine or a placebo and measures the rate of infection. Which type of study design is this?

Accepted Answer

Experimental study

Question 16

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

Accepted Answer

$$\dfrac{1}{3}$$

Question 17

A hospital wants to know if the recovery time after surgery is normally distributed. Which graphical method is most appropriate to assess normality?

Accepted Answer

Normal probability plot (Q-Q plot)

Question 18

A researcher wants to test if the observed frequencies of blood types in a population match the expected frequencies. Which statistical test should be used?

Accepted Answer

Chi-square goodness-of-fit test

Question 19

A study finds that the correlation between exercise frequency and cholesterol level is $$r = -0.60. $$What does this mean?

Accepted Answer

There is a moderate negative linear relationship between exercise frequency and cholesterol level.

Question 20

A researcher collects data on the number of defective products produced each day for a month. Which type of data is this?

Accepted Answer

Discrete quantitative data

Statistical Reasoning: Course Syllabus and Study Guide

Guida di studio - Domande di pratica

Study guide - Flashcard