Question 1

Which of the following best describes a histogram?

Accepted Answer

A graph that displays the frequency of data within equal intervals using bars.

Question 2

When constructing a histogram, what is the first step you should take?

Accepted Answer

Determine the number of bins (classes) and their width.

Question 3

A histogram is constructed for the heights of 100 students. The bars are not touching each other. What does this indicate?

Accepted Answer

The data is likely categorical, not continuous.

Question 4

Which of the following is NOT a characteristic of a histogram?

Accepted Answer

It shows the relationship between two variables.

Question 5

Given the following data: 2, 3, 3, 4, 5, 5, 5, 6, 7, construct a histogram with bin width 2. Which bin will have the highest frequency?

Accepted Answer

$$[4,6)$$

Question 6

Which of the following statements about scatterplots is TRUE?

Accepted Answer

Scatterplots are used to display the relationship between two quantitative variables.

Question 7

A researcher plots the heights and weights of 50 adults on a scatterplot. What can be inferred if the points form a pattern that rises from left to right?

Accepted Answer

There is a positive correlation between height and weight.

Question 8

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

Accepted Answer

$$r = \frac{n\sum x_iy_i - \sum x_i \sum y_i}{\sqrt{[n\sum x_i^2$ - (\sum x_i)^2$][n\sum y_i^2$ - (\sum y_i)^2$]}}$$

Question 9

If the linear correlation coefficient $$r = 0.85$$ for a dataset, which of the following best describes the relationship between the variables?

Accepted Answer

There is a strong positive linear relationship.

Question 10

A medical researcher tests a new drug and obtains a P-value of $$0.03. If $$the significance level is $$\alpha = 0.05$$, what should the researcher conclude?

Accepted Answer

Reject the null hypothesis; there is significant evidence the drug is effective.

Question 11

Which of the following best interprets a P-value?

Accepted Answer

The probability of obtaining a result as extreme as, or more extreme than, the observed result, assuming the null hypothesis is true.

Question 12

Given a dataset with $$n = 20$$ pairs of data and a calculated $$r = 0.45$$, which of the following is the correct critical value for $$r at$$ $$\alpha = 0.05 ($$two-tailed)?

Accepted Answer

$$r_{critical} \approx 0.444$$

Question 13

A scatterplot of hours studied and exam scores shows a downward trend. What does this indicate?

Accepted Answer

There is a negative correlation between hours studied and exam scores.

Question 14

Which of the following is a key difference between a histogram and a scatterplot?

Accepted Answer

A histogram displays the distribution of a single variable, while a scatterplot shows the relationship between two variables.

Question 15

If the calculated $$r$$ value is greater than the critical value, what is the correct conclusion?

Accepted Answer

There is a statistically significant linear relationship between the variables.

Question 16

A histogram of annual incomes in a city is skewed to the right. What does this suggest about the distribution?

Accepted Answer

Most people earn lower incomes, with a few earning much higher incomes.

Question 17

Which of the following is the correct formula for the P-value in a hypothesis test for a mean (assuming normality)?

Accepted Answer

$$P = P(|Z| \u003e |z_{obs}|)$$

Question 18

Which scenario best illustrates the use of a scatterplot?

Accepted Answer

Analyzing the relationship between daily temperature and ice cream sales.

Question 19

If a histogram has a single peak and is roughly symmetric, which distribution does it most likely represent?

Accepted Answer

Normal distribution

Introductory Statistics Study Guide: Histograms, Scatterplots, P-values, and Correlation

Guida di studio - Domande di pratica

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