Q: To determine if there are outliers in the forehead length data, which formula should you use for the upper and lower fences?

$$\displaystyle Q_1$ - 1.5 \times IQR$$ and $$Q_3 + 1.5$$ \times IQR$$

Question 1

Given the forehead length data: 5.5, 5.6, 5.4, 5.5, 5.7, 4.7, 4.8, 4.9, 4.7, 5.6, 5.8, 5.9, 6.1, 6.0, 4.3, 4.7, 4.9, 6.3, 4.9, 5.6, 5.4, 5.6, 5.5, 5.2, 5.1, 5.7, 5.8, 5.9, 5.8, 6.1, what is the correct frequency for the interval $$4.2 - 4.6$$?

Accepted Answer

1

Question 2

What is the shape of the forehead length data distribution based on the histogram and summary statistics?

Accepted Answer

Skewed right

Question 3

Calculate the mean (average) forehead length for the given data set. (Round to two decimal places)

Accepted Answer

$$\displaystyle 5.48$$

Question 4

Given the forehead length data, what is the median value?

Accepted Answer

$$\displaystyle 5.55$$

Question 5

If the mean forehead length is greater than the median, what does this suggest about the shape of the data?

Accepted Answer

The data is skewed right

Question 6

Which of the following is the correct five-number summary for the forehead length data? (Values are rounded to the nearest tenth)

Accepted Answer

$$\displaystyle 4.3, 4.8, 5.5, 5.9, 6.3$$

Question 7

To determine if there are outliers in the forehead length data, which formula should you use for the upper and lower fences?

Accepted Answer

$$\displaystyle Q_1$ - 1.5 	imes IQR$$ and $$Q_3 + 1.5$$ 	imes IQR$$

Question 8

Dr. Burner finds that the age of onset of hair loss is normally distributed with mean $$38$$ and standard deviation $$3. $$What percentage of men begin hair loss between ages $$34$$ and $$45$$? (Use the empirical rule)

Accepted Answer

$$\displaystyle 95\%$$

Question 9

For the same normal distribution (mean $$38$$, SD $$3$$), what is the percentage of men who begin hair loss after age $$37$$?

Accepted Answer

$$\displaystyle 63\%$$

Question 10

For the normal distribution of age of hair loss onset (mean $$38$$, SD $$3$$), what is the percentage of men who begin hair loss before age $$40$$?

Accepted Answer

$$\displaystyle 84\%$$

Question 11

At what age is a man at the 90th percentile for hair loss onset, given a normal distribution with mean $$38$$ and SD $$3$$? (Use $$z = 1.28$$ for the 90th percentile)

Accepted Answer

$$\displaystyle 41.8$$

Question 12

Given the data on duration of drug on scalp (in minutes) and hair growth (in inches), which of the following best describes the correlation between the two variables?

Accepted Answer

Strong positive correlation

Question 13

Suppose the line of best fit for the drug duration and hair growth data is $$y = 0.25x + 0.3. $$What does the slope $$0.25$$ represent in this context?

Accepted Answer

For each additional minute, hair growth increases by $$0.25$$ inches

Question 14

Using the line of best fit $$y = 0.25x + 0.3$$, what is the predicted hair growth for $$8$$ minutes of drug application?

Accepted Answer

$$\displaystyle 2.3$$ inches

Question 15

If the actual hair growth at $$4$$ minutes is $$1.3$$ inches, and the predicted value from the line of best fit $$y = 0.25x + 0.3 is$$ $$1.3$$ inches, what is the residual?

Accepted Answer

$$\displaystyle 0$$

Question 16

If the coefficient of determination $$R^2$$ for the regression is $$0.85$$, what does this mean?

Accepted Answer

85% of the variation in hair growth is explained by the duration of drug application

Question 17

Given the following counts for hair growth by age group: 35-39 (Yes: 67, No: 35), 40-44 (Yes: 118, No: 45), 45-49 (Yes: 75, No: 54), 50-54 (Yes: 38, No: 68), what is the marginal distribution for the 40-44 age group?

Accepted Answer

$$\displaystyle \frac{163}{600}$$

Question 18

What is the conditional probability that a participant aged 45-49 experienced hair growth?

Accepted Answer

$$\displaystyle \frac{75}{129}$$

Question 19

What percentage of 40-44-year-olds did NOT regrow their hair? (Round to the nearest percent)

Accepted Answer

$$\displaystyle 28\%$$

Question 20

If Dr. Burner only invited his immediate family to participate in the study, what type of bias would this introduce?

Accepted Answer

Selection bias

Question 21

To obtain a representative sample of 2000 people from hair clubs across the US, which sampling method should Dr. Burner use?

Accepted Answer

Simple random sampling

Step-by-Step Guidance for Statistics Review: Dr. Burner's Baldness Study

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