12 exercises · 12 automatically checked · Untimed
12 questions · Shuffled order · Untimed practice
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A recipe uses flour and sugar in the ratio 7 : 3. If it uses 420 grams of flour, how many grams of sugar does it use?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 180 The scale factor is 420/7
Ratios and proportions / Standard Review: Data reference.
A vehicle travels 18 kilometers in 15 minutes at a constant speed. What is its speed in kilometers per hour?
Answer: A / 72 Fifteen minutes is one-quarter hour. The rate is 18/(1/4)
Rates and units / Standard Review: Example 2.13.
A price rises from $80 to $92. What is the percent increase?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 15 The increase is 12, measured relative to the original 80. Thus (12/80)(100)
Percent change / Standard Review: Example 2.02.
The dot plot shows seven observations. What is their median?
Answer: B / 4 The ordered observations are 1, 2, 2, 4, 4, 4, 7. The fourth observation, the middle of seven, is 4. Dot height gives frequency, not a separate data value.
One-variable data / Standard Review: Data reference.
Ten observations have mean 16. One observation of value 38 is added. What is the new mean?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 18 The original total is 10(16)
Means and totals / Standard Review: Example 6.13.
Every value in a data set is multiplied by 3. Which statement must be true?
Answer: A / The standard deviation is multiplied by 3. Multiplying all values by positive 3 multiplies the mean and every deviation from that mean by 3. Hence the standard deviation also triples.
Spread and transformations / Standard Review: Example 2.11.
A fitted line is = 2.4x + 11. What is its predicted value of y at x = 15?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 47 Substitute the input: 2.4(15) + 11 = 36 + 11 = 47. This is the model prediction, not a guarantee about an individual observation.
Two-variable models / Standard Review: Example 2.09.
The table summarizes club participation. A student who plays chess is selected at random. What is the probability that the student also plays tennis?
Tennis | No tennis | |
|---|---|---|
Chess | 12 | 18 |
No chess | 8 | 22 |
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 2/5 There are 12 + 18
Conditional probability / Standard Review: Example 2.08.
A bag contains 5 green and 7 yellow counters. Two are selected without replacement. What is the probability that both are green?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 5/33 The first-green probability is 5/12. After a green is removed, 4 green counters remain among 11 counters. Multiply: (5/12)(4/11) = 20/132 = 5/33.
Probability without replacement / Challenge Review: Example 6.14.
In a random sample of 200 residents, 74 support a proposal. Using this sample, estimate the number of supporters among 5000 residents.
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 1850 The sample rate is 74/200
Population inference / Standard Review: Example 2.15.
A sample estimate is 61% with a margin of error of 5 percentage points. What is the lower endpoint of the reported interval, as a percent?
Answer: A / 56 Subtract the margin in percentage points: 61 − 5
Margin of error / Standard Review: Example 5.08.
A random sample of a town is surveyed about exercise and sleep. An association is found. Which conclusion is justified by the design alone?
Answer: C / The sample can inform an association estimate for the town, but not a causal conclusion. Random sampling supports generalization to the sampled population, with uncertainty. Without randomized treatment assignment, the association does not establish causation.
Study design / Standard Review: Example 1.13.
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