Question 1

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

Accepted Answer

Descriptive statistics summarize and display data, while inferential statistics use data from a sample to make generalizations about a population.

Question 2

A researcher wants to estimate the average height of all university students. She measures the heights of 100 randomly selected students. In this context, what is the sample and what is the population?

Accepted Answer

Sample: 100 measured students; Population: all university students.

Question 3

Which of the following is a common statistical fallacy?

Accepted Answer

Assuming that correlation implies causation.

Question 4

Suppose a study finds a strong positive correlation between ice cream sales and drowning incidents. Which of the following is the most appropriate conclusion?

Accepted Answer

There may be a lurking variable, such as temperature, causing both to increase.

Question 5

A pharmaceutical company tests a new drug on a sample of 200 patients and finds that 160 show improvement. Construct a point estimate for the proportion of all patients who would improve with the drug.

Accepted Answer

$$ \frac{160}{200} = 0.8 $$

Question 6

Which of the following is the correct formula for the sample variance $$ s^2$  of a $$data set with $$ n $$ observations $$ x_1$, x_2$, ..., x_n $$ and sample mean $$ \bar{x} $$?

Accepted Answer

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

Question 7

A hospital administrator wants to know if a new scheduling system reduces patient wait times. She collects data before and after implementation. Which statistical method is most appropriate to test if the new system is effective?

Accepted Answer

Hypothesis testing for the difference in means.

Question 8

Which of the following graphical displays is most appropriate for showing the distribution of a single quantitative variable, such as the ages of patients in a clinic?

Accepted Answer

Histogram

Question 9

A confidence interval for a population mean is given by $$ (\bar{x} - E, \bar{x} + E) . If$$ $$ \bar{x} = 50 $$ and $$ E = 4 $$, what is the confidence interval?

Accepted Answer

$$ (46, 54) $$

Question 10

Which of the following statements about probability is correct?

Accepted Answer

The probability of an event is always between 0 and 1, inclusive.

Question 11

A researcher wants to test whether a coin is fair. She flips the coin 100 times and gets 60 heads. Which of the following is the correct null hypothesis $$ H_0$ $$ for this test?

Accepted Answer

$$ H_0$: p = 0.5 $$

Question 12

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 13

A study reports a 95% confidence interval for the mean systolic blood pressure in adults as $$ (120, 130) . $$Which of the following is the correct interpretation?

Accepted Answer

We are 95% confident that the true mean systolic blood pressure in adults is between 120 and 130.

Question 14

Which of the following is NOT a measure of center?

Accepted Answer

Range

Question 15

A data set has a mean of 20 and a standard deviation of 4. What is the z-score of a value $$ x = 28 $$? Use the formula $$ z = \frac{x - \mu}{\sigma} .$$

Accepted Answer

$$ z = 2 $$

Question 16

Which of the following is the correct formula for the probability of the union of two mutually exclusive events $$ A $$ and $$ B $$?

Accepted Answer

$$ P(A \cup B) = P(A) + P(B) $$

Question 17

A scatterplot of two variables shows a downward trend. Which of the following best describes the relationship?

Accepted Answer

There is a negative correlation between the variables.

Question 18

A researcher is interested in the effect of a new teaching method on student performance. She randomly assigns students to two groups: one uses the new method, the other uses the traditional method. What type of study design is this?

Accepted Answer

Experimental study

Question 19

Which of the following is a correct statement about bias in statistical studies?

Accepted Answer

Bias can lead to systematic errors in the results of a study.

Question 20

A medical researcher wants to estimate the average cholesterol level in a population. She collects a random sample and calculates a 99% confidence interval. Compared to a 95% confidence interval, the 99% interval will be:

Accepted Answer

Wider, because higher confidence requires a larger margin of error.

Math 1123-OL: Statistics – Course Syllabus and Overview

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