Question 1

Which of the following best describes the purpose of the Central Limit Theorem in statistics?

Accepted Answer

It allows us to use the Normal distribution to approximate the distribution of sample means, regardless of the population's distribution, as sample size increases.

Question 2

A pharmaceutical company wants to compare the effectiveness of two drugs. Which statistical method should they use to determine if there is a significant difference in mean effectiveness between the two drugs?

Accepted Answer

Inference for two samples to compare population means

Question 3

Which of the following is a source of bias in sample surveys?

Accepted Answer

Nonrandom errors such as undercoverage or response bias

Question 4

Suppose a researcher constructs a boxplot for exam scores. What information does the boxplot NOT directly provide?

Accepted Answer

The exact values of all individual scores

Question 5

A hospital wants to estimate the proportion of patients who recover within 7 days after surgery. Which formula should they use to construct a confidence interval for the population proportion, assuming a large sample?

Accepted Answer

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

Question 6

Which of the following best explains Simpson’s paradox?

Accepted Answer

A relationship between variables reverses when data are combined across groups.

Question 7

In a simple linear regression model, what does the coefficient of determination ($$ R^2$ ) $$represent?

Accepted Answer

The proportion of variance in the dependent variable explained by the independent variable.

Question 8

A researcher is concerned about making a Type I error in a significance test. What does a Type I error mean?

Accepted Answer

Rejecting a true null hypothesis.

Question 9

Which of the following is the correct formula for the residual standard error in a simple linear regression model?

Accepted Answer

$$ \sqrt{\frac{\sum (y_i - \hat{y}_i)^2$}{n-2}} $$

Question 10

A scientist wants to test whether the mean weight of a new species of fish is different from 10 kg. Which statistical test should they use?

Accepted Answer

Significance testing for a single mean

Question 11

Which sampling design is most likely to reduce bias in a survey about student satisfaction at a university?

Accepted Answer

Random sampling

Question 12

A medical researcher collects data on blood pressure and cholesterol levels for 100 patients. Which statistical method is most appropriate to measure the strength and direction of the linear relationship between these two variables?

Accepted Answer

Correlation

Question 13

Which formula is used to calculate the sample variance?

Accepted Answer

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

Question 14

A school administrator wants to know if a new teaching method improves test scores. She randomly assigns students to two groups: one uses the new method, the other uses the traditional method. What is this type of study called?

Accepted Answer

Experimental design

Question 15

Which formula is used to calculate a confidence interval for a population mean when the sample size is small and the population standard deviation is unknown?

Accepted Answer

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

Question 16

A researcher wants to predict the mean response for a given value of the independent variable in a simple linear regression model. Which interval should they construct?

Accepted Answer

Confidence interval for the mean response

Question 17

Which of the following is NOT a descriptive measure of spread?

Accepted Answer

Median

Question 18

A survey is conducted to estimate the average time students spend studying per week. The sample mean is 15 hours, the sample standard deviation is 4 hours, and the sample size is 36. What is the 95% confidence interval for the population mean?

Accepted Answer

$$ 15 \pm 1.96 	imes \frac{4}{\sqrt{36}} $$

Question 19

Which of the following best describes blocking in experimental design?

Accepted Answer

Grouping subjects with similar characteristics to reduce variability within treatment groups.

Math 105: Basic Probability and Statistics – Course Syllabus and Study Guide

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