Q: How many degrees of freedom are used in the chi-square test for the poverty table?

$$ (r-1) \times (c-1) = (4-1) \times (2-1) = 3 $$

Q: Given the regression output for hospital stay, what is the equation of the regression line?

$$ \text{Hospital Stay} = 0.515681 + 1.28997 \times \text{Surgery Time} $$

Question 1

A researcher wants to determine if there is a significant difference in the average cost of haircuts between two salons: Hair by Charles and Curl Up & Dye. Which inference procedure should be used, and what assumptions must be checked before proceeding?

Accepted Answer

A two-sample t-test for independent means; check for independence, normality, and equal variances.

Question 2

Given the output for the two-sample t-test for Hair by Charles vs Curl Up & Dye, what is the correct interpretation of the p-value?

Accepted Answer

There is not enough evidence at the usual significance level to conclude a difference in mean haircut costs between the two salons.

Question 3

In the poverty table, what is the correct null hypothesis for the chi-square test?

Accepted Answer

There is no association between region and poverty status.

Question 4

How many degrees of freedom are used in the chi-square test for the poverty table?

Accepted Answer

$$ (r-1) 	imes (c-1) = (4-1) 	imes (2-1) = 3 $$

Question 5

Given the regression output for hospital stay, what is the equation of the regression line?

Accepted Answer

$$ 	ext{Hospital Stay} = 0.515681 + 1.28997 	imes 	ext{Surgery Time} $$

Question 6

What does the coefficient for Surgery Time in the hospital stay regression output represent?

Accepted Answer

For each additional hour of surgery, the hospital stay increases by about 1.29 days.

Question 7

In the regression analysis for Reading CTBS vs Math CTBS, what is the interpretation of the R-squared value?

Accepted Answer

About 79% of the variation in reading scores is explained by math scores.

Question 8

Based on the scatterplot and residuals plot for Reading CTBS vs Math CTBS, are the assumptions for regression satisfied?

Accepted Answer

Yes, the residuals appear randomly scattered and the histogram is roughly symmetric.

Question 9

For the tax advice table, which statistical test is most appropriate to determine if tax advice is associated with paying a lower percentage of taxes?

Accepted Answer

Chi-square test for independence

Question 10

Given the two-sample t-test output for SET M1 vs SET M2, what is the correct conclusion?

Accepted Answer

There is significant evidence that the mean of SET M2 is greater than the mean of SET M1.

Question 11

In the context of the table for test identification, which procedure should be used for comparing the mean of differences in matched pairs?

Accepted Answer

Mean of differences - matched pairs, t-test, degrees of freedom = $$ n-1 $$

Question 12

For the chi-square test on attitudes toward cloning and education level, how is the expected count for the first cell calculated?

Accepted Answer

$$ 	ext{Expected count} = \frac{	ext{Row total} 	imes 	ext{Column total}}{	ext{Grand total}} $$

Question 13

Given the regression output for car reliability vs price, what is the interpretation of the slope coefficient?

Accepted Answer

For each unit increase in price, reliability increases by about 0.51 units.

Question 14

In the regression analysis for weight vs height, what does the value of s represent?

Accepted Answer

The standard deviation of the residuals, indicating the typical error in predicting weight from height.

Question 15

Based on the scatterplot, residuals plot, and histogram for weight vs height, are the assumptions for regression satisfied?

Accepted Answer

Yes, the residuals are randomly scattered and the histogram is roughly symmetric.

Question 16

For the employment program table, which statistical test is most appropriate to determine if the help program is associated with employment status?

Accepted Answer

Chi-square test for independence

Question 17

Given the two-sample t-test output for SET C1 vs SET C2, what is the correct conclusion?

Accepted Answer

There is significant evidence that the mean sulfate level after scrubbers (C2) is lower than before (C1).

Question 18

In the regression output for weight vs length of carnivores, what is the equation of the regression line?

Accepted Answer

$$ 	ext{Weight} = -668.3 + 485.21 	imes 	ext{Length} $$

Statistical Inference and Regression Analysis: Practice with Real Data Outputs

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