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This quiz was administered in-person. It was closed-book and closed-note; students were not allowed to use the DSC 10 Reference Sheet. Students had 20 minutes to work on the quiz.

This quiz covered Lectures 17-19 of the Spring 2024 offering of DSC 10.

Note (groupby / pandas 2.0): Pandas 2.0+ no longer silently drops columns that can’t be aggregated after a groupby, so code written for older pandas may behave differently or raise errors. In these practice materials we use .get() to select the column(s) we want after .groupby(...).mean() (or other aggregations) so that our solutions run on current pandas. On real exams you will not be penalized for omitting .get() when the old behavior would have produced the same answer.

Problem 1

Problem 1.1

Suppose that the trees on UCSD’s campus have a mean height of 100 feet and a variance of 36 feet. If the height of a specific tree is 124 feet, what would its height be in standard units for this distribution? Simplify your answer.

Problem 1.2

Let A be the answer to the previous question. Choose the best interpretation of A.

• A randomly selected tree on UCSD’s campus has an A percent probability of being at least 124 feet tall.

• A 124 foot tree is A times taller than the average tree on UCSD’s campus.

• A 124 foot tree is A standard deviations taller than the average tree on UCSD’s campus.

• At least 95% of trees on UCSD’s campus have a height within A standard deviations of the mean height.

Problem 2

You are told that scipy.stats.norm.cdf(-1.4) evaluates to 0.08075665923377107. Suppose you have a standard normal curve with mean at x=0 and standard deviation 1. What is the area under the curve from x=0 to x=1.4? Give your answer as a number rounded to 2 decimal places.

Problem 3

Suppose we measure the height in feet of a sample of trees on UCSD’s campus and use this sample to generate a 95% CLT-based confidence interval for the mean height of trees on campus. Let W be the width of this confidence interval.

If we instead were to measure the height of the same sample in inches, and again generate a 95% CLT-based confidence interval for the mean, what would be the width of this confidence interval in terms of W? There are 12 inches in 1 foot.

• \dfrac{W}{12}

• \dfrac{W}{\sqrt{12}}

• W

• 12W

• 144W

Problem 4

Which of the following quantities must be known in order to construct a CLT-based confidence interval for the population mean? Select all that apply.

• Shape of the population (normal or not)

• Shape of the sample (normal or not)

• Mean of the population

• Mean of the sample

• Standard deviation of the population

• Standard deviation of the sample

• Size of the population

• Size of the sample

Problem 5

We want to collect a sample of trees and use this sample to determine the proportion of all trees that are oak trees (a population parameter). We want to create a 95% confidence interval that is at most 0.04 wide. Which of the following inequalities should we use to find the smallest viable sample size we could collect?

• \text{sample size} \geq (4 * \frac{0.5}{0.04})^2

• \text{sample size} \geq (2 * \frac{0.5}{0.04})^2

• \text{sample size} \geq (4 * \frac{1}{0.04})^2

• \text{sample size} \geq (2 * \frac{1}{0.04})

Problem 6

Suppose that the trees on UCSD’s campus are 35% eucalyptus, 25% pine, and the remaining 40% some other variety. Write one line of code to simulate the act of randomly sampling 40 trees from this distribution, with replacement. Your code should output an array of length 3 where the elements represent the number of eucalyptus, pine, and other trees, respectively.

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