C955: Applied Probability and Statistics
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Free C955: Applied Probability and Statistics Questions
A company wants to compare the quarterly profits for two consecutive years. The profits are given in the table.
Which graphical displays would be most appropriate for visualizing these data?
Explanation
Explanation
The correct graph is the last graph since it shows each quarter side by side making it easy to visually interpret the data.
Correct Answer
Which combination of factors is most likely to result in a significant outcome for a hypothesis test?
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A small sample size and a small variance
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A small sample size and a large variance
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A large sample size and a small variance
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A large sample size and a large variance
Explanation
Explanation:
The power of a hypothesis test increases with larger sample sizes and lower variance because these factors reduce the standard error and make it easier to detect true effects. A large sample size provides more information about the population, while small variance indicates more consistency within the data, both of which enhance the likelihood of finding statistical significance when a true effect exists.
Correct Answer:
A large sample size and a small variance
A classroom survey recorded the number of pets owned by each student: 5 students have 0 pets, 8 students have 1 pet, 4 students have 2 pets, and 3 students have 3 pets. Which type of graph would best represent the frequency of pets owned by students?
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A line graph with points connected to show changes in pet ownership over time
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A bar graph with bars showing the number of students for each pet count
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A pie chart with slices representing the proportion of each pet count
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A scatterplot with points showing the relationship between pet count and student age
Explanation
Explanation:
The data provided shows the number of students corresponding to each number of pets, which is categorical frequency data. A bar graph is ideal for displaying frequency distributions because each category (number of pets) can be represented by a separate bar, making it easy to compare the number of students in each category. Line graphs and scatterplots are better for trends or relationships over time or between variables, and pie charts show proportions but are less precise for comparing counts.
Correct Answer:
A bar graph with bars showing the number of students for each pet count
Measures the risk of dying during the first year of life
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Neonatal mortality rate
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Fetal death rate
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Infant mortality rate
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Maternal mortality rate
Explanation
Explanation:
The measure that specifically assesses the likelihood of a baby dying before reaching one year of age is the infant mortality rate. This rate is calculated as the number of deaths of infants under one year old per 1,000 live births in a given year. It captures all deaths within the first year, not just specific periods such as the neonatal stage.
Correct Answer:
Infant mortality rate
A study investigates the effect of study hours on exam scores among college students.
Which statement describes the relationship between study hours and exam scores?
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Study hours are the explanatory variable, while exam scores are the response variable.
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Both study hours and exam scores are explanatory variables.
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Both study hours and exam scores are response variables.
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Exam scores are the explanatory variable, while study hours are the response variable.
Explanation
Explanation:
In this study, the goal is to examine how study hours influence exam scores. Study hours are the independent variable (explanatory variable) because they are manipulated or measured to see their effect. Exam scores are the dependent variable (response variable) because they respond to changes in study hours.
Correct Answer:
Study hours are the explanatory variable, while exam scores are the response variable.
In a study assessing the percentage of students who own an Ampple smartphone, if a researcher wants to test whether the ownership rate is significantly different from 70%, which of the following scenarios would require the same null and alternative hypotheses as stated in the provided question?
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Testing if the ownership rate is less than 70%.
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Testing if the ownership rate is greater than 70%.
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Testing if the ownership rate is exactly 70%
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Testing if the ownership rate is different from 70%
Explanation
Explanation:
The original question tests whether the ownership rate is significantly different from 70%, which represents a two-tailed hypothesis test. The null hypothesis is that the population proportion equals 70%, and the alternative hypothesis is that the proportion does not equal 70%. The scenario that would require the same null and alternative hypotheses is one that also tests for a difference, not a specific direction such as greater than or less than. Therefore, testing if the ownership rate is different from 70% matches the original question’s hypotheses.
Correct Answer:
Testing if the ownership rate is different from 70%.
In a raffle, the probability of winning a gift card (Event A) is 0.2, and the probability of winning a free ticket (Event B) is 0.3.
What is the probability of winning either a gift card or a free ticket?
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0.1
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0.25
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0.5
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0.6
Explanation
Explanation:
Assuming the events are mutually exclusive (a participant cannot win both), the probability of winning either a gift card or a free ticket is:
P(A or B) = P(A) + P(B) = 0.2 + 0.3 = 0.5
Correct Answer:
0.5
A sample of 150 new cell phones produced by Yeskia found that 12 had cosmetic flaws. A 90% confidence interval for the proportion of all new Yeskia phones with cosmetic flaws is 0.044 to 0.116. Which statement below provides the correct interpretation of this confidence interval?
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none of the above
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There is a 90% chance that the proportion of new phones that have cosmetic flaws is between 0.044 and 0.116
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There is at least a 4.4% chance that a new phone will have a cosmetic flaw
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If you selected a very large number of samples and constructed a confidence interval for each, 90% of these intervals would include the proportion of all new phones with cosmetic flaws.
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A sample of 150 phones will have no more than 11.6% with cosmetic flaws.
Explanation
Explanation:
A confidence interval represents a range of plausible values for the population proportion based on the sample data. The correct interpretation is that if we were to take a very large number of samples and calculate a 90% confidence interval from each, approximately 90% of those intervals would contain the true population proportion. It does not indicate the probability that the proportion for a single sample lies within the interval.
Correct Answer:
If you selected a very large number of samples and constructed a confidence interval for each, 90% of these intervals would include the proportion of all new phones with cosmetic flaws.
If x = 15, evaluate the following expression:
x · (x − 7)
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8
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105
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120
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225
Explanation
Explanation:
We substitute x = 15 into the expression x · (x − 7).
x · (x − 7) = 15 · (15 − 7)
= 15 · 8
= 120
Correct Answer:
C. 120
The following figure shows the scatter plot showing the amount of rainfall and the number of trains canceled in a city for 12 separate years.
What is the approximate correlation coefficient and interpretation of the correlation between the variables?
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−0.5 and a moderate negative correlation
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0.6 and a moderate positive correlation
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0.6 and a strong positive correlation
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0.1 and a weak positive correlation
Explanation
Explanation
The scatterplot shows an upward trend: as the amount of rainfall increases, the number of trains canceled also increases. The points are moderately close to the trend line, indicating a moderate positive correlation. The correlation coefficient is approximately 0.6.
Correct Answer
B. 0.6 and a moderate positive correlation
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