Question 1

Which of the following scenarios is most appropriate for using a Chi-square test for independence?

Accepted Answer

Testing whether the preference for a type of cuisine is related to gender.

Question 2

Given the following observed and expected counts for a Chi-square goodness of fit test: Observed = [30, 14], Expected = [33, 11], what is the calculated Chi-square statistic?

Accepted Answer

$$\$$chi^2$$ = \sum \frac{(O-E)^2$}{E} = \frac{(30-33)^2$}{33} + \frac{(14-11)^2$}{11} = 0.2727 + 0.8182 = 1.0909$$

Question 3

What is the null hypothesis for a Chi-square test for independence?

Accepted Answer

The two variables are independent.

Question 4

Which formula correctly represents the Chi-square statistic?

Accepted Answer

$$\$$chi^2$$ = \sum \frac{(O-E)^2$}{E}$$

Question 5

A Pearson correlation coefficient $$r of 0.93 $$was found between daily new COVID-19 cases and daily new deaths. What does this indicate?

Accepted Answer

There is a strong positive linear relationship between daily new cases and daily new deaths.

Question 6

Which of the following is NOT an assumption of the Chi-square test?

Accepted Answer

Data are measured on an interval or ratio scale.

Question 7

In the context of regression, what does the equation $$y = 0.01859x + 21.22561$$ represent?

Accepted Answer

A linear model predicting daily new deaths from daily new cases.

Question 8

Which of the following best describes the range of Pearson's correlation coefficient $$r$$?

Accepted Answer

$$-1 \u003c r \u003c 1$$

Question 9

A researcher wants to test if the distribution of blood types in a city matches the national distribution. Which statistical test should be used?

Accepted Answer

Chi-square goodness of fit test

Question 10

If the calculated Chi-square statistic is less than the critical value at $$\alpha = 0.05$$, what is the correct conclusion?

Accepted Answer

Fail to reject the null hypothesis

Question 11

Which of the following is a correct interpretation of $$r = 0 in $$Pearson's correlation?

Accepted Answer

There is no linear relationship between the two variables.

Question 12

Which of the following is NOT a use of the Chi-square test?

Accepted Answer

Testing the linear relationship between two continuous variables.

Question 13

A study finds $$r = -1$$ between two variables. What does this mean?

Accepted Answer

There is a perfect negative linear relationship.

Question 14

Which plot is most appropriate to visualize the relationship between two continuous variables?

Accepted Answer

Scatter plot

Question 15

In a Chi-square test for independence, what does a significant result indicate?

Accepted Answer

There is evidence that the two categorical variables are associated.

Question 16

Which of the following statements about correlation and regression is TRUE?

Accepted Answer

Correlation measures the strength and direction of a linear relationship, while regression predicts the value of one variable based on another.

Question 17

A Chi-square test for independence is performed on the relationship between preference for the shape of roti canai and gender. The p-value is 0.03. What is the correct interpretation at $$\alpha = 0.05$$?

Accepted Answer

There is a statistically significant association between preference for roti canai shape and gender.

Question 18

Which of the following is a requirement for using Pearson's correlation coefficient?

Accepted Answer

Both variables must be interval or ratio scale and approximately normally distributed.

Question 19

If a regression equation is $$y = 0.01859x + 21.22561$$, what is the predicted value of $$y$$ when $$x = 1000$$?

Accepted Answer

$$y = 0.01859 	imes 1000 + 21.22561 = 18.59 + 21.22561 = 39.81561$$

Association: Chi-Square Tests, Correlation, and Linear Regression

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