Question 1

Which of the following best describes the shape of a histogram representing the distribution of exam scores where most students scored high, but a few scored very low?

Accepted Answer

The histogram is left-skewed.

Question 2

A researcher collects data on the heights of 100 students and wants to construct a histogram. Which step should be performed first?

Accepted Answer

Determine the class intervals.

Question 3

Which characteristic is NOT typically represented in a histogram?

Accepted Answer

Individual data values

Question 4

Given the following paired data: (2, 5), (3, 7), (4, 9), (5, 11), which scatterplot pattern would you expect?

Accepted Answer

A positive linear relationship

Question 5

Which of the following statements about scatterplots is TRUE?

Accepted Answer

Scatterplots display the relationship between two quantitative variables.

Question 6

A scatterplot of the relationship between hours studied and exam score shows points clustered along a straight line sloping upward. What does this indicate?

Accepted Answer

There is a positive correlation between hours studied and exam score.

Question 7

If a histogram of household incomes is right-skewed, what does this imply about the distribution?

Accepted Answer

Most households have low incomes.

Question 8

Which formula is used to calculate the linear correlation coefficient $$r$$ for paired data $$(x_i, y_i)$$?

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 9

A P-value is calculated in a hypothesis test. Which interpretation is correct?

Accepted Answer

The P-value is the probability of obtaining a result as extreme as the observed, assuming the null hypothesis is true.

Question 10

You are given paired data and calculate $$r = 0.85$$ for the linear correlation coefficient. If the critical value is $$0.75$$, what can you conclude?

Accepted Answer

There is a significant linear correlation.

Question 11

Which of the following is NOT a step in constructing a histogram?

Accepted Answer

Connect the tops of the bars with lines.

Question 12

A scatterplot shows a random pattern of points with no discernible trend. What does this suggest about the relationship between the two variables?

Accepted Answer

There is no correlation.

Question 13

If the linear correlation coefficient $$r is $$calculated as $$-0.92$$, what does this indicate?

Accepted Answer

There is a strong negative linear relationship.

Question 14

Which of the following best describes a bimodal histogram?

Accepted Answer

A histogram with two distinct peaks.

Question 15

A medical researcher wants to analyze the relationship between age and blood pressure. Which graphical tool should they use?

Accepted Answer

Scatterplot

Question 16

If a histogram is constructed with too few classes, what is a likely consequence?

Accepted Answer

The histogram will obscure important features of the data.

Question 17

A scatterplot of the relationship between temperature and ice cream sales shows a strong positive trend. Which real-world conclusion can be drawn?

Accepted Answer

Higher temperatures are associated with higher ice cream sales.

Question 18

Which of the following is the correct formula for the critical value of the linear correlation coefficient for $$n$$ pairs at significance level $$\alpha$$?

Accepted Answer

$$r_{critical} = \frac{t_{\alpha/2}}{\sqrt{n-2 + t_{\alpha/2}^2}}$$

Question 19

A P-value of $$0.03 is $$obtained in a test of a new drug's effectiveness. If the significance level is $$0.05$$, what should the researcher conclude?

Accepted Answer

Reject the null hypothesis.

STA2023 Quiz 2: Histograms, Scatterplots, and Correlation Guidance

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