Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

Statistic

Question 3

Which of the following is NOT a characteristic of a well-designed statistical study?

Accepted Answer

Use of anecdotal evidence

Question 4

A researcher wants to compare the mean cholesterol levels between two groups: those who exercise regularly and those who do not. Which statistical method is most appropriate?

Accepted Answer

Two-sample t-test

Question 5

Which formula correctly calculates the sample mean $$\bar{x}$$ for a dataset with $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$

Question 6

A study finds a correlation coefficient $$r = 0.85$$ between hours studied and exam scores. Which of the following best describes this relationship?

Accepted Answer

There is a strong positive linear relationship.

Question 7

Which of the following statements about observational studies is TRUE?

Accepted Answer

Observational studies can identify associations but not causation.

Question 8

Suppose you want to estimate the proportion of voters who support a new policy. You survey 500 randomly selected voters and find that 320 support the policy. What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \frac{320}{500} = 0.64$$

Question 9

Which of the following best describes the margin of error in a confidence interval?

Accepted Answer

The range of values within which the true parameter is expected to lie, with a certain level of confidence.

Question 10

A hospital wants to compare the average recovery times for two treatments. The mean recovery time for Treatment A is 5 days ($$n=40$$, $$s=1.2$$), and for Treatment B is 6 days ($$n=35$$, $$s=1.5). $$Which formula would you use to calculate the standard error for the difference in means?

Accepted Answer

$$SE = \sqrt{\frac{s_A^2$}{n_A} + \frac{s_B^2$}{n_B}}$$

Question 11

Which of the following is an example of a categorical variable?

Accepted Answer

Favorite color

Question 12

A researcher calculates a 95% confidence interval for the mean systolic blood pressure in a population as (120, 130). What does this interval mean?

Accepted Answer

We are 95% confident that the population mean lies between 120 and 130.

Question 13

Which formula is used to calculate the sample variance $$s^2$$ for a dataset with $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$ and sample mean $$\bar{x}$$?

Accepted Answer

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

Question 14

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

Accepted Answer

To make a decision about a population parameter based on sample data.

Question 15

A scientist wants to test whether a new fertilizer increases plant growth. She randomly assigns 50 plants to receive the fertilizer and 50 plants to not receive it. What type of study is this?

Accepted Answer

Experimental study

Question 16

Which of the following is the correct formula for the confidence interval for a population mean when the population standard deviation is unknown?

Accepted Answer

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

Question 17

A student wants to summarize the relationship between two quantitative variables: hours of sleep and test scores. Which graphical display is most appropriate?

Accepted Answer

Scatterplot

Question 18

Which of the following statements about statistical significance is TRUE?

Accepted Answer

Statistical significance means the result is unlikely to have occurred by chance.

Question 19

A medical researcher wants to estimate the mean blood glucose level in diabetic patients. She collects a random sample of 100 patients and calculates a sample mean of 150 mg/dL with a sample standard deviation of 20 mg/dL. What is the standard error of the mean?

Accepted Answer

$$SE = \frac{20}{\sqrt{100}} = 2$$

Question 20

Which of the following best describes the concept of independent events in probability?

Accepted Answer

The occurrence of one event does not affect the probability of the other.

STA 147: Introduction to Statistics – Syllabus and Study Guide

Study Guide - Practice Questions

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