# Fall 2023 Quiz 4

← return to practice.dsc10.com

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 18-22 of the Fall 2023 offering of DSC 10.

Video streaming services, such as Netflix and Hulu, are more popular than ever. Let’s investigate trends in the video streaming habits of UCSD students.

## Problem 1

You survey 100 DSC majors and 140 CSE majors to ask them which video streaming service they use most. The resulting distributions are given in the table below. Note that each column sums to 1.

Service DSC Majors CSE Majors
Netflix 0.4 0.35
Hulu 0.25 0.2
Disney+ 0.1 0.1
Amazon Prime Video 0.15 0.3
Other 0.1 0.05

For example, 20% of CSE Majors said that Hulu is their most used video streaming service. Note that if a student doesn’t use video streaming services, their response is counted as Other.

### Problem 1.1

What is the total variation distance (TVD) between the distribution for DSC majors and the distribution for CSE majors? Give your answer as an exact decimal.

Answer: 0.15

##### Difficulty: ⭐️⭐️

The average score on this problem was 89%.

### Problem 1.2

Suppose we only break down video streaming services into four categories: Netflix, Hulu, Disney+, and Other (which now includes Amazon Prime Video). Now we recalculate the TVD between the two distributions. How does the TVD now compare to your answer to part (a)?

• less than (a)

• equal to (a)

• greater than (a)

Answer: less than (a)

##### Difficulty: ⭐️

The average score on this problem was 93%.

## Problem 2

You want to estimate the proportion of DSC majors who have a Netflix subscription. To do so, you will survey a random sample of DSC majors and ask them whether they have a Netflix subscription. You will then create a 95% confidence interval for the proportion of “yes" answers in the population, based on the responses in your sample. You decide that your confidence interval should have a width of at most 0.10.

### Problem 2.1

In order for your confidence interval to have a width of at most 0.10, the standard deviation of the distribution of the sample proportion must be at most T. What is T? Give your answer as an exact decimal.

Answer: 0.025

##### Difficulty: ⭐️⭐️⭐️⭐️

The average score on this problem was 46%.

### Problem 2.2

Using the fact that the standard deviation of any dataset of 0s and 1s is no more than 0.5, calculate the minimum number of people you would need to survey so that the width of your confidence interval is at most 0.10. Give your answer as an integer.

Answer: 400

##### Difficulty: ⭐️⭐️

The average score on this problem was 81%.

## Problem 3

Arya was curious how many UCSD students used Hulu over Thanksgiving break. He surveys 250 students and finds that 130 of them did use Hulu over break and 120 did not.

Using this data, Arya decides to test following hypotheses:

• Null Hypothesis: Over Thanksgiving break, an equal number of UCSD students did use Hulu and did not use Hulu.

• Alternative Hypothesis: Over Thanksgiving break, more UCSD students did use Hulu than did not use Hulu.

### Problem 3.1

Which of the following could be used as a test statistic for the hypothesis test?

• The proportion of students who did use Hulu minus the proportion of students who did not use Hulu.

• The absolute value of the proportion of students who did use Hulu minus the proportion of students who did not use Hulu.

• The proportion of students who did use Hulu plus the proportion of students who did not use Hulu.

• The absolute value of the proportion of students who did use Hulu plus the proportion of students who did not use Hulu.

Answer: The proportion of students who did use Hulu minus the proportion of students who did not use Hulu.

##### Difficulty: ⭐️⭐️

The average score on this problem was 81%.

### Problem 3.2

For the test statistic that you chose in part (a), what is the observed value of the statistic? Give your answer either as an exact decimal or a simplified fraction.

Answer: 0.04

##### Difficulty: ⭐️

The average score on this problem was 90%.

### Problem 3.3

If the p-value of the hypothesis test is 0.053, what can we conclude, at the standard 0.05 significance level?

• We reject the null hypothesis.

• We fail to reject the null hypothesis.

• We accept the null hypothesis.

Answer: We fail to reject the null hypothesis.

##### Difficulty: ⭐️⭐️

The average score on this problem was 87%.