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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 14-17 of the Fall 2023 offering of DSC 10.

Ciro is an avid fan of Costco, a members-only warehouse store. On his recent trip to the Morena Boulevard location near campus, he was surprised by how full shoppers’ carts were and was inspired to investigate how much people typically spend at Costco.

Problem 1

Among all Costco members in San Diego, the average monthly spending in October 2023 was $350 with a standard deviation of $40.

Problem 1.1

The amount Ciro spent at Costco in October 2023 was -1.5 in standard units. What is this amount in dollars? Give your answer as an integer.

Problem 1.2

What is the minimum possible percentage of San Diego members that spent between $250 and $450 in October 2023?

• 16%

• 22%

• 36%

• 60%

• 78%

• 84%

Problem 1.3

Now, suppose we’re given that the distribution of monthly spending in October 2023 for all San Diego members is roughly normal. Given this fact, fill in the blanks:

What are m and n? Give your answers as integers rounded to the nearest multiple of 10.

Problem 2

Suppose we have access to a simple random sample of all US Costco members of size 145. Our sample is stored in a DataFrame named us_sample, in which the "Spend" column contains the October 2023 spending of each sampled member in dollars.

Problem 2.1

Fill in the blanks:

• sample statistic; population parameter

• population statistic; sample parameter

• sample parameter; population statistic

• population parameter; sample statistic

Problem 2.2

Fill in the blanks below so that us_left and us_right are the left and right endpoints of a 46% confidence interval for the average October 2023 spending of all US members.

costco_means = np.array([])
for i in np.arange(5000):
    resampled_spends = __(x)__
    costco_means = np.append(costco_means, resampled_spends.mean())
left = np.percentile(costco_means, __(y)__)
right = np.percentile(costco_means, __(z)__)

Which of the following could go in blank (x)? Select all that apply.

• us_sample.sample(145, replace=True).get("Spend")

• us_sample.sample(145, replace=False).get("Spend")

• np.random.choice(us_sample.get("Spend"), 145)

• np.random.choice(us_sample.get("Spend"), 145, replace=True)

• np.random.choice(us_sample.get("Spend"), 145, replace=False)

• None of the above.

What goes in blanks (y) and (z)? Give your answers as integers.

Problem 2.3

True or False: 46% of all US members in us_sample spent between left and right in October 2023.

• True

• False

Problem 2.4

True or False: If we repeat the code from part (b) 200 times, each time bootstrapping from a new random sample of 145 members drawn from all US members, then about 92 of the intervals we create will contain the average October 2023 spending of all US members.

• True

• False

Problem 2.5

True or False: If we repeat the code from part (b) 200 times, each time bootstrapping from us_sample, then about 92 of the intervals we create will contain the average October 2023 spending of all US members.

• True

• False

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