Question 1

Which of the following best describes a categorical variable?

Accepted Answer

A variable that represents categories or groups, such as eye color or type of car.

Question 2

A researcher wants to study the effect of a new medication on blood pressure. She randomly assigns 100 patients to either the medication or a placebo group. What type of study design is this?

Accepted Answer

Experimental study

Question 3

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 4

Which of the following is NOT a characteristic of a simple random sample?

Accepted Answer

Selection of one individual affects the selection of another.

Question 5

A histogram is best used to display which type of data?

Accepted Answer

Numerical data

Question 6

Which of the following is the correct formula for the standard deviation $$s of a $$sample?

Accepted Answer

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

Question 7

A boxplot is useful for identifying which of the following?

Accepted Answer

The presence of outliers

Question 8

Which of the following best describes the Central Limit Theorem?

Accepted Answer

The distribution of sample means approaches normality as sample size increases, regardless of the population distribution.

Question 9

Suppose a dataset has a mean of 50 and a standard deviation of 5. What is the z-score for a value of 60?

Accepted Answer

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

Question 10

Which of the following is a correct interpretation of a 95% confidence interval for a population mean?

Accepted Answer

If we took many samples, about 95% of the calculated intervals would contain the population mean.

Question 11

Which formula is used to calculate 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 12

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

Accepted Answer

Linear regression

Question 13

Which of the following statements about outliers is correct?

Accepted Answer

Outliers can have a large effect on the mean and standard deviation.

Question 14

Which formula is used to calculate the probability of event $$A in a $$sample space $$S$$?

Accepted Answer

$$P(A) = \frac{n(A)}{n(S)}$$

Question 15

A 95% confidence interval for a population mean is calculated as $$\bar{x} \pm 1.96 \frac{s}{\sqrt{n}}. $$What does the value 1.96 represent?

Accepted Answer

The critical value from the standard normal distribution for 95% confidence

Question 16

Which of the following best describes a double-blind experiment?

Accepted Answer

Neither the subjects nor the experimenters know which treatment each subject receives.

Question 17

Which formula is used to calculate the standard error of the mean for a sample of size $$n$$ with standard deviation $$s$$?

Accepted Answer

$$SE = \frac{s}{\sqrt{n}}$$

Question 18

A p-value is best described as:

Accepted Answer

The probability of observing data as extreme as, or more extreme than, the observed data, assuming the null hypothesis is true.

Question 19

Which of the following is a correct interpretation of a Type I error in hypothesis testing?

Accepted Answer

Rejecting the null hypothesis when it is true.

Question 20

Which formula is used to calculate the margin of error for a confidence interval for a population proportion $$\hat{p}$$ with sample size $$n$$?

Accepted Answer

$$ME = z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

STAT 1000: Basic Statistical Analysis 1 – Syllabus and Course Outline Study Guide

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