Applied Healthcare & Health Fitness — AQ01 Applied Healthcare Statistics C784 Version 1
Answer: D
1/5 x 3/4 equals 3/20.
To find the product of 1/5 and 3/4, multiply the numerators together and the denominators together, resulting in 3/20.
A) 4/9
Option A is incorrect because multiplying 1/5 by 3/4 does not yield 4/9. The correct multiplication process does not support this result, as neither 4 nor 9 appear in the calculation of the product.
B) 4/20
Option B is incorrect. While the denominator is correct when simplifying, the numerator is not. The product of the numerators (1 and 3) is 3, not 4, making 4/20 an invalid result for this multiplication.
C) 3/9
Option C is also incorrect. The product 3/9 suggests an incorrect numerator, as the multiplication of 1/5 and 3/4 results in 3, but the denominator should not be 9. The correct denominator from the multiplication is 20, not 9.
D) 3/20
Option D is correct. When multiplying 1/5 and 3/4, the numerators (1 and 3) multiply to give 3, and the denominators (5 and 4) multiply to give 20, resulting in the correct answer of 3/20.
Conclusion
The correct answer, 3/20, is derived directly from the multiplication of the fractions 1/5 and 3/4. All other options fail to reflect the proper calculations, either through incorrect numerators or denominators, confirming that D is the definitive answer to the question.
2. What is the value of x in the following equation? 4(x - 3) = 8 - x
Answer: C
The value of x in the equation 4(x - 3) = 8 - x is 4.
To solve for x, we can simplify the equation. Distributing the 4 gives us 4x - 12 = 8 - x. Adding x to both sides and 12 to both sides leads us to 5x = 20, resulting in x = 4.
A) 2
This option is incorrect. If we substitute x with 2 in the equation, we have 4(2 - 3) = 8 - 2, which simplifies to -4 = 6, a false statement.
B) 3
This option is also incorrect. Substituting x with 3 gives us 4(3 - 3) = 8 - 3, simplifying to 0 = 5, which is not true.
C) 4
This option is correct. Substituting x with 4 in the original equation results in 4(4 - 3) = 8 - 4, simplifying to 4 = 4, which is true.
D) 5
This option is incorrect as well. If we substitute x with 5, we find 4(5 - 3) = 8 - 5, which simplifies to 8 = 3, a false statement.
Conclusion
The correct answer is 4, as substituting this value into the original equation holds true. All other options fail to satisfy the equation, demonstrating that they are not valid solutions. This reinforces the importance of correctly manipulating and solving algebraic equations to find accurate values.
Answer: D
Conditional percentages are the appropriate numerical measure for the study.
Conditional percentages provide a clear understanding of the relationship between blood pressure readings and the use of a continuous positive airway pressure machine among sleep apnea patients. This measure allows for the comparison of proportions within different groups based on their usage of the machine.
A) Regression analysis
Regression analysis is used to determine the relationship between independent and dependent variables, often predicting outcomes based on certain factors. However, it is not the best choice for summarizing the most common blood pressure readings among distinct groups, as the study aims to compare proportions rather than establish predictive relationships.
B) Five-number summary
The five-number summary provides a quick overview of a dataset through its minimum, first quartile, median, third quartile, and maximum. While it offers useful information about the distribution of blood pressure readings, it does not specifically address the comparison between sleep apnea patients who use the CPAP machine and those who do not, making it less suitable for this study.
C) Correlation coefficient
The correlation coefficient measures the strength and direction of a relationship between two variables. In this context, it would not effectively summarize the blood pressure readings between the two distinct groups, as it does not provide a comparison of proportions or frequencies necessary for the study's objective.
D) Conditional percentages
Conditional percentages allow for the analysis of the proportion of patients within each group (CPAP users and non-users) who fall into specific blood pressure categories. This measure effectively captures the comparative aspect of the study by showing how blood pressure readings differ between the two groups.
Conclusion
Conditional percentages are the most appropriate choice for this study as they provide a clear comparative measure of blood pressure readings among different groups. Other options, like regression analysis, five-number summary, and correlation coefficients, do not adequately fulfill the requirement to analyze and compare the proportions of blood pressure readings in relation to CPAP machine usage. Thus, D is the correct answer.
4. What is 3/4 divided by 2/3?
Answer: B
3/4 divided by 2/3 equals 9/8.
To find the result of 3/4 divided by 2/3, you multiply 3/4 by the reciprocal of 2/3, which is 3/2. This calculation yields 9/8.
A) 1/2
This option is incorrect because dividing 3/4 by 2/3 does not yield a fraction that simplifies to 1/2. Instead, the operation leads to a larger fraction, as shown in the correct calculation.
B) 9/8
This is the correct answer. When dividing 3/4 by 2/3, you multiply by the reciprocal (3/2), resulting in (3/4) * (3/2) = 9/8. This fraction is greater than 1, which aligns with the expected outcome of the division.
C) 8/9
This option is incorrect because the division of 3/4 by 2/3 does not simplify to 8/9. Instead, it reflects a misunderstanding of the operation, as the result should be greater than 1.
D) 5/12
This choice is also incorrect. The fraction 5/12 does not represent the outcome of dividing 3/4 by 2/3. The correct calculation leads to a fraction that is larger than both 3/4 and 2/3.
Conclusion
The correct answer, 9/8, is derived from the proper application of the division of fractions, specifically by multiplying by the reciprocal. All other options fail to represent the correct mathematical outcome of this division operation, demonstrating a clear understanding of fraction manipulation is essential.
Answer: D
Those with high BMI are more likely to be non-exercisers because 58.8% is greater than 42.3%.
The data indicates that a higher percentage of non-exercisers have a high BMI compared to exercisers. Specifically, 58.8% of non-exercisers fall into the high BMI category, which is significantly greater than the 42.3% of exercisers who are categorized as having a high BMI.
A) Those with high BMI are less likely to be non-exercisers because 41.2% is less than 42.3%.
This option is incorrect because it misinterprets the relationship between BMI and exercise. The percentage of non-exercisers with low BMI (41.2%) does not directly influence the likelihood of having a high BMI; rather, the relevant comparison is between the high BMI percentages of non-exercisers and exercisers.
B) Those with high BMI are less likely to be non-exercisers because 57.7% is less than 58.8%.
This option is also incorrect. While it correctly identifies the percentages, it misinterprets the data's implications. The statement suggests that a lower percentage of exercisers with low BMI indicates a lesser likelihood of non-exercisers having high BMI, which is a flawed interpretation of the data.
C) Those with high BMI are less likely to be non-exercisers because 58.8% is greater than 41.2%.
This option is misleading. Although it accurately states that 58.8% is greater than 41.2%, it incorrectly concludes that this supports a lesser likelihood of non-exercisers having a high BMI. The relevant comparison should be between the high BMI percentages of both groups, not just the low BMI percentages.
D) Those with high BMI are more likely to be non-exercisers because 58.8% is greater than 42.3%.
This option is correct. It highlights that a greater percentage of non-exercisers (58.8%) have a high BMI compared to exercisers (42.3%). This indicates a stronger association between being a non-exerciser and having a high BMI, which is supported by the data.
Conclusion
The correct interpretation of the data shows that non-exercisers are more likely to have a high BMI, as indicated by the higher percentage of non-exercisers (58.8%) falling into this category compared to exercisers (42.3%). The other options either misinterpret the relationships or present comparisons that do not support the conclusions drawn from the data. Thus, option D is the definitive answer.
6. What are the principal square roots of 64 and 16?
Answer: A
The principal square roots of 64 and 16 are 8 and 4.
The square root of 64 is 8, and the square root of 16 is 4, making these values the principal square roots of the respective numbers.
A) 8 and 4
This option is correct because the principal square root of 64 is indeed 8, and the principal square root of 16 is 4. Both values are non-negative and accurately represent the square roots of the provided numbers.
B) 32 and 8
This option is incorrect. While 8 is the correct square root of 16, 32 is not a square root of 64. The square root of 64 is 8, not 32; hence this pair does not satisfy the question.
C) 4 and 16
This option is also incorrect. The number 4 is the square root of 16, but 16 is not a square root of 64; rather, it is the original number. The correct square root of 64 is 8, making this option invalid.
D) 8 and 2
This option is incorrect as well. Although 8 is the correct square root of 64, 2 is not a square root of 16. The principal square root of 16 is 4, not 2, which makes this option false.
Conclusion
Option A is definitively correct as it accurately identifies the principal square roots of 64 and 16 as 8 and 4, respectively. All other options fail to provide the correct roots, either presenting incorrect values or misidentifying the square roots of the given numbers.
Answer: D
Box Plot effectively displays the median hours slept.
A Box Plot is the most suitable graphic representation for showing the median number of hours slept, as it visually summarizes the distribution of the data, including the median, quartiles, and potential outliers.
A) Histogram
A histogram is used to depict the frequency distribution of numerical data. While it can provide insights into the data's distribution, it does not specifically highlight the median, which is a key requirement for this analysis.
B) Bar chart
A bar chart is typically used for categorical data, comparing different groups or categories. It does not effectively show measures of central tendency like the median and is therefore not suitable for this dataset of hours slept.
C) Pie chart
A pie chart is designed to show the proportions of a whole, making it ideal for categorical data rather than continuous numerical data. It does not provide any information about the median or distribution of hours slept, rendering it ineffective for this purpose.
D) Box Plot
A Box Plot is specifically designed to display the distribution of numerical data and highlights the median, making it the most appropriate choice for this dataset. It allows for a clear visualization of the data's central tendency and variability.
Conclusion
The Box Plot is the definitive choice for representing the median hours slept, as it effectively summarizes the dataset while providing crucial information about the median and overall distribution. In contrast, the other options fail to focus on the median or are unsuitable for continuous numerical data, making them less effective for this analysis.
8. Which percentage of patients had esophageal or skin cancer?
Answer: B
23% of patients had esophageal or skin cancer.
The data indicates that 23% of patients were diagnosed with either esophageal or skin cancer, highlighting a significant prevalence of these conditions within the patient population.
A) 1%
This option is incorrect as it underrepresents the prevalence of esophageal or skin cancer among patients. The percentage is significantly higher according to the data provided.
B) 23%
This option is correct, as it accurately reflects the data indicating that 23% of patients were diagnosed with esophageal or skin cancer. This percentage is a crucial statistic for understanding the impact of these cancers within the patient group.
C) 32%
Choosing 32% is incorrect as it overestimates the prevalence of esophageal or skin cancer among the patients. The actual figure is lower, indicating a need for more accurate data interpretation.
D) 45%
This option is also incorrect, as it significantly overstates the percentage of patients with esophageal or skin cancer. The actual data shows a lower prevalence, making this choice inaccurate.
Conclusion
The correct answer is 23%, which directly reflects the provided data on patient diagnoses. All other options fail to accurately represent the statistics, either underestimating or overestimating the prevalence of esophageal or skin cancer among the patients. Understanding this correct figure is essential for evaluating the health impact of these conditions.
Answer: A
Mode is the appropriate numerical measure.
The mode is the most frequent value in a dataset, making it ideal for identifying the most common blood pressure reading among patients who consumed more than 10 alcoholic beverages in a week.
A) Mode
The mode is the correct choice because it specifically identifies the value that appears most frequently in a given set of data. In this study, the goal is to determine the most frequent blood pressure reading, which is precisely what the mode provides.
B) Median
The median refers to the middle value in a dataset when arranged in ascending order. While it offers insight into the central tendency of the data, it does not indicate which blood pressure reading occurs most frequently, making it less suitable for this specific study.
C) Correlation coefficient
The correlation coefficient measures the strength and direction of the relationship between two variables. In this context, it does not apply as the study is focused on identifying a single measure of blood pressure, not examining relationships between variables.
D) Conditional percentages
Conditional percentages compare proportions within specific categories. However, this measure does not provide information about the most frequent blood pressure reading, thus failing to address the primary objective of the study.
Conclusion
The mode is definitively the right answer as it directly fulfills the requirement to identify the most frequent blood pressure reading in the study. All other options either address different statistical concepts or do not provide the necessary information concerning frequency, which is the core focus of the question.
10. What effect would removing the outlier have on the relationship between variable 1 and variable 2?
Answer: A
Removing the outlier would weaken the positive relationship between variable 1 and variable 2.
Eliminating an outlier can lead to a more accurate representation of the correlation between two variables. In this case, the presence of the outlier may have artificially inflated the perceived strength of the positive relationship.
A) It would weaken the positive relationship
This option is correct because removing an outlier often clarifies the true nature of the relationship between the variables. If the outlier was significantly influencing the correlation, its removal can reveal a less robust positive relationship than previously observed.
B) It would strengthen the positive relationship
This option is incorrect. If an outlier is contributing to a perceived strength in the positive relationship, its removal would not strengthen this relationship. Instead, it would likely reveal that the true correlation is weaker than initially indicated.
C) It would strengthen the neutral relationship
This option is also incorrect. The term "neutral relationship" suggests that there is no significant correlation between the two variables. Removing an outlier would not strengthen a neutral relationship, as there is nothing to enhance if no correlation exists.
D) It would weaken the neutral relationship
This option is incorrect as well. A neutral relationship implies no correlation; hence, the removal of an outlier would have no effect on the strength of that relationship, as it does not exist to begin with.
Conclusion
In conclusion, removing the outlier would weaken the positive relationship because it allows for a more accurate assessment of the correlation between variable 1 and variable 2. The other options fail to recognize that the presence of an outlier may distort the perceived strength of relationships, making them less reliable.