**Question 1:**
Two owners of a cattle ranch, Robert and Val, want to find the average weight for the ranch's 200 cows. Instead of weighing all of the cows:
- Robert weighs 25 cows and gets an average weight of 1,550 pounds (standard deviation = 50).
- Val weighs 100 cows and gets an average weight of 1,380 pounds (standard deviation = 50).

What is Val's margin of error, rounded to the nearest whole number?
(Use the formula: \(1.96 \times \frac{\text{standard deviation}}{\sqrt{N}}\))

A. 2.45
B. 1.01
C. 9.80
D. 3.92

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**Question 2:**
An article reports that men over 6 feet tall earn more than men under 6 feet, with these numbers:
- Average salary of 6-foot-plus males: $55,000
- Average salary of males under 6 feet: $47,000
- p-value: 0.45

Based on that reported p-value, and using the common definition of "statistical significance," which is the case?

A. The salary differences are statistically significant.
B. The salary differences are not statistically significant.
C. With that p-value, the results are not significant.
D. With that p-value, the differences are very close, but not statistically significant.

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**Question 3:**
Database A contains 40 data items, made up equally of the values 0 and 100, and has a mean of 50.
Database B also has 40 entries, made up equally of the values 49 and 51, and also has a mean of 50.

Which database will have the smaller value for its standard deviation?

A. Not enough information provided to answer.
B. They will have the same standard deviation.
C. Database A
D. Database B

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**Question 4:**
If a study determines the difference in average salary for subpopulations of mechanical engineers and civil engineers is NOT significant, then the subpopulations of mechanical and civil engineers are:

A. Guaranteed not to be earning differently
B. Not earning differently
C. Earning very similarly
D. Definitely earning the same

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**Question 5:**
Given the following true statements, select the best logical induction made from them:
- Betsy likes oranges.
- Jose does not like oranges.
- Benjamin likes oranges.

A. People do and do not like oranges.
B. People only like oranges.
C. People like apples and oranges.
D. People like all fruit.

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**Question 6:**
Given:
- If X, then not Y.
- If not Y, then Z.
- Y is true.

So:

A. X is unknown, Z is true.
B. X is false, Z is unknown.
C. X is unknown, Z is unknown.
D. X is true, Z is true.

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**Question 7:**
Using a standard six-sided die, Janice rolled either a 2 or a 5 on the last 6 rolls of the die. What is the probability of Janice rolling a 2 or a 5 on her 7th toss of the die?

A. \( \frac{2}{7} \)
B. \( \frac{1}{7} \)
C. \( \frac{1}{3} \)
D. \( \frac{1}{6} \)

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**Question 8:**
Estimate the average by first rounding to the nearest 100: 120, 230, 455, 175

A. 225
B. 275
C. 250
D. 202.50

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**Question 9:**
A lock consists of 4 dials, where each dial has 6 letters. What is the probability of guessing the right combination in one try?

A. \( \frac{1}{6} \)
B. \( \frac{1}{1296} \)
C. \( \frac{1}{256} \)
D. \( \frac{1}{24} \)

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**Question 10:**
A restaurant will select 1 card from a bowl to win a free lunch. Jimmy puts 10 cards in the bowl. The bowl has a total of 150 cards in it when they do the drawing. What are the odds of Jimmy winning a free lunch?

A. \( \frac{1}{10} \)
B. \( \frac{3}{20} \)
C. \( \frac{1}{150} \)
D. \( \frac{1}{15} \)

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**Question 11:**
What is the average of the following numbers? 2, 5, 8, 1

A. 5
B. 4.5
C. 4
D. 3

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**Question 12:**
Both sets of values have an average of 13. Is Set A's standard deviation smaller, larger, or about the same as Set B's?
(Note: This question can be answered by knowing the concept of standard deviation, without actually computing the standard deviation).

Set A: 1, 2, 3, 23, 24, 25
Set B: 9, 10, 11, 14, 16, 18

A. About the same
B. Smaller
C. Not enough information provided to tell
D. Larger

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**Question 13:**
A slot machine has 3 dials. Each dial has 40 positions, two of which are "Jackpot." To win the jackpot, all three dials must be in the "Jackpot" position. Assuming each play spins the dials and stops each independently and randomly, what are the odds of one play winning the jackpot?

A. \( \frac{1}{27} \) (0.037 = 3.7%)
B. \( \frac{1}{64000} \) (0.00014 = 0.014%)
C. \( \frac{1}{64000} \) (0.0000156 = 0.00156%)
D. \( \frac{1}{8000} \) (0.000125 = 0.0125%)

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**Question 14:**
What is the median of these figure skating ratings? 5.0, 6.0, 7.0, 7.5, 8.0, 9.0, 10.0

A. 3.0
B. 6.0
C. 7.5
D. 7.14

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**Question 15:**
A bag of the same size small balls contains 6 blue balls, 5 red balls, 5 yellow balls, and 4 green balls. What is the probability of selecting a blue or green ball on the first draw?

A. \( \frac{1}{2} \)
B. \( \frac{9}{20} \)
C. \( \frac{2}{5} \)
D. \( \frac{1}{10} \)

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**Question 16:**
A medication states that the odds of having an allergic reaction are 2 in 200. What is that probability stated as a percent?

A. 2%
B. 1%
C. 4%
D. 5%