C955: Applied Probability and Statistics
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Free C955: Applied Probability and Statistics Questions
A company sends a survey out to managers and non management employees asking if the company should switch to a new healthcare plan.
|
|
For |
Against |
Total |
|
Managers |
35 |
15 |
50 |
|
Non-management Employees |
75 |
325 |
400 |
The results of the survey are shown in the 2 × 2 contingency table below:Which statement is true?
-
A manager is slightly less likely than a nonmanager to want to switch plans.
-
A manager is much more likely than a nonmanager to want to switch plans.
-
A manager is much less likely than a nonmanager to want to switch plans.
-
A manager is slightly more likely than a nonmanager to want to switch plans.
Explanation
Correct answer
B. A manager is much more likely than a nonmanager to want to switch plans.
Explanation
Option B correctly represents the survey results. To see this clearly, calculate the percentage for both groups: Managers who want to switch = %, Nonmanagers who want to switch = %. Comparing these percentages, managers (70%) are significantly more likely than nonmanagers (18.75%) to want to switch healthcare plans, clearly justifying the statement that managers are much more likely to favor switching.
The box and whisker plot shows the battery life of two smartphones under the same usage conditions.
Which statement is true about the median battery life of Model X and Model Y?
-
The median battery life of Model X is higher than that of Model Y.
-
It is not possible to compare the median battery life of Model X and Model Y.
-
The median battery life of Model Y is higher than that of Model X.
-
The median battery life of Model X and Model Y is the same.
Explanation
Explanation:
The median of a boxplot is represented by the line inside the box. For Model X, the median line is at approximately 6 hours, while for Model Y, the median line is at approximately 8 hours. Comparing these medians shows that Model Y has a higher median battery life than Model X.
Correct Answer:
The median battery life of Model Y is higher than that of Model X.
A researcher has collected information on participants at a marathon and wants to display the ages of the runners:
16, 25, 36, 27, 48, 35, 26, 57, 45, 35, 66, 47, 28, 34, 25, 48
Which graph type should be used to display these data?
-
Bar graph
-
Stem-and-leaf plot
-
Line graph
-
Pie chart
Explanation
Correct answer
b. Stem-and-leaf plot
Explanation
The correct answer is option b, Stem-and-leaf plot, because it effectively organizes numerical data by displaying both distribution and individual data values. It clearly shows the frequency of ages while preserving original numerical data. A stem-and-leaf plot is ideal for relatively small datasets, allowing a clear visual representation of the spread and central tendency of the data.
If the combined number of students enrolled in music and art is 100, what is the total number of students enrolled in the elective subjects?
-
250
-
300
-
380
-
700
Explanation
Explanation:
From the pie chart:
Music = 26%
Art = 14%
So, Music + Art = 40% of the total.
We are told this 40% equals 100 students.
That means the total number of students is:
100 ÷ 0.40 = 250
Correct Answer:
A. 250
A quality control inspector finds that 0.7% of the light bulbs produced at a factory are faulty. What is the probability that a randomly chosen light bulb made at the factory is not faulty?
-
30%
-
50%
-
93%
-
99.3%
Explanation
Explanation:
The probability that a light bulb is not faulty is the complement of it being faulty.
Probability(not faulty) = 1 − Probability(faulty)
= 1 − 0.007
= 0.993 or 99.3%
Correct Answer:
99.3%
What is the definition of a null hypothesis (Ho) in the context of hypothesis testing?
-
A statement that there is no effect or no difference
-
A statement that indicates a significant effect or difference
-
A prediction about the outcome of an experiment
-
A conclusion drawn from statistical analysis
Explanation
Explanation:
The null hypothesis is a formal statement that there is no effect, no change, or no difference in the population parameter being tested. It serves as the default or baseline assumption that researchers attempt to test against. Statistical tests evaluate whether the observed data provide enough evidence to reject this assumption.
Correct Answer:
A statement that there is no effect or no difference.
A market research study was conducted to learn more about pet ownership and veterinary visits. Subjects were classified as pet owners or non-pet owners.
|
Results |
Visit Veterinarians |
Do not Visit Veterinarians |
Total |
|
Pet Owners |
80% |
20% |
100% |
|
Non-pet Owners |
10% |
90% |
100% |
How can these data be interpreted?
-
Pet owners are more likely to visit veterinarians because 80% is greater than 20%.
-
Pet owners are more likely to visit veterinarians because 80% is greater than 80%.
-
Pet owners are more likely to visit veterinarians because 80% is greater than 10%.
-
Pet owners are more likely to visit veterinarians because 80% is greater than 100%.
Explanation
Explanation:
The comparison should be made between pet owners (80%) and non-pet owners (10%) who visit veterinarians. The 80% of pet owners visiting veterinarians is significantly higher than the 10% of non-pet owners, indicating that pet owners are more likely to visit veterinarians.
Correct Answer:
Pet owners are more likely to visit veterinarians because 80% is greater than 10%.
An investigation is being conducted to assess the impact of sleep duration on cognitive performance in teenagers.
Which statement describes the relationship between sleep duration and cognitive performance?
-
Cognitive performance is the explanatory variable, while sleep duration is the response variable
-
Sleep duration is the explanatory variable, while cognitive performance is the response variable
-
Both sleep duration and cognitive performance are explanatory variables
-
Both sleep duration and cognitive performance are response variables
Explanation
Explanation
The explanatory variable (independent variable) is the factor that is manipulated or observed to see its effect on another variable. Here, sleep duration affects cognitive performance, so sleep duration is the explanatory variable, and cognitive performance is the response variable.
Correct Answer
B. Sleep duration is the explanatory variable, while cognitive performance is the response variable
If five dice are thrown, what is the probability that the sum of the numbers appearing on them is 30? Assume the same conditions as before
-
1/7776
-
0
-
1/6
-
1/1296
Explanation
Explanation:
The maximum possible sum when throwing five six-sided dice is 6 × 5 = 30. There is exactly one outcome that achieves this total: all five dice must show 6. The total number of equally likely outcomes is 6⁵ = 7776. Therefore, the probability is 1 out of 7776.
Correct Answer:
1/7776
A jar contains marbles numbered 1 through 25.
What is the probability of drawing a 10 first, and then a prime number greater than 1 without replacement?
Explanation
Explanation
Step 1: Probability of drawing 10 first = 1/25
Step 2: After removing 10, there are 24 marbles left. Prime numbers greater than 1 between 1 and 25: 2, 3, 5, 7, 11, 13, 17, 19, 23 → 9 primes
Probability of drawing a prime next = 9/24 = 3/8
Combined probability = (1/25) × (3/8) = 3/200
Correct Answer
A. 3/200
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