Q: Which formula is used to calculate the expected count in a cell for a chi-square test of independence?

$$ \dfrac{(\text{Row Total}) \times (\text{Column Total})}{\text{Grand Total}} $$

Question 1

A hospital is testing a new drug and wants to know if the recovery rate differs between patients who receive the drug and those who do not. Which statistical test is most appropriate to analyze the association between treatment and recovery status?

Accepted Answer

A chi-square test of independence

Question 2

Which of the following best describes the meaning 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 3

A researcher wants to estimate the proportion of students who prefer online learning. She surveys 200 students and finds that 120 prefer online learning. Construct a 95% confidence interval for the proportion. Which formula should she use?

Accepted Answer

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

Question 4

Which of the following is NOT an assumption for performing a chi-square test of independence?

Accepted Answer

The data are normally distributed

Question 5

In a clinical trial, the risk ratio (RR) for developing a side effect in the treatment group compared to the control group is calculated as 2.0. What does this mean?

Accepted Answer

The treatment group is twice as likely to develop the side effect as the control group

Question 6

Which of the following best describes a Type II error in hypothesis testing?

Accepted Answer

Failing to reject the null hypothesis when it is false

Question 7

A study finds a statistically significant association between smoking and lung cancer with a p-value of 0.001. Which statement is most accurate?

Accepted Answer

There is strong evidence against the null hypothesis of no association

Question 8

Which formula is used to calculate the expected count in a cell for a chi-square test of independence?

Accepted Answer

$$ \dfrac{(	ext{Row Total}) 	imes (	ext{Column Total})}{	ext{Grand Total}} $$

Question 9

A pharmaceutical company wants to test if a new drug is more effective than the standard treatment. They set up a hypothesis test with $$ \alpha = 0.05 . $$What does $$ \alpha $$ represent?

Accepted Answer

The probability of making a Type I error

Question 10

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

Accepted Answer

If we repeated the study many times, about 95% of the calculated intervals would contain the true population mean

Question 11

In an experiment, what is the primary purpose of random assignment?

Accepted Answer

To eliminate confounding variables and ensure groups are comparable

Question 12

A researcher calculates the odds ratio (OR) for a disease in exposed vs. unexposed groups and finds $$ OR = 1 . $$What does this indicate?

Accepted Answer

Exposure does not affect the odds of disease

Question 13

Which of the following is NOT a principle of experimental design?

Accepted Answer

Correlation

Question 14

A study reports a statistically significant result but with a very small effect size. What is the best conclusion?

Accepted Answer

The result is statistically significant but may not be practically important

Question 15

Which formula is used to calculate the power of a statistical test?

Accepted Answer

$$ 1 - \beta $$

Question 16

A school wants to know if the distribution of students across four majors is uniform. Which chi-square test should be used?

Accepted Answer

Chi-square test of goodness-of-fit

Question 17

Which of the following best describes the complement of an event $$ A  in $$probability?

Accepted Answer

All outcomes in the sample space that are not in $$ A $$

Question 18

A researcher wants to compare the effect of two diets on weight loss. She randomly assigns participants to each diet and measures their weight loss after 8 weeks. What type of study is this?

Accepted Answer

Experimental study

Question 19

Which formula correctly applies the addition rule for two mutually exclusive events $$ A $$ and $$ B $$?

Accepted Answer

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

Statistics Study Guide: Probability, Experimental Design, Chi-Square Tests, and Statistical Inference

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