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Chamberlain University
MATH-225 Statistical Reasoning for the Health Sciences
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The sampling method employed for the Week 5 lab assignment to collect height data was convenience sampling. This nonrandom method involves gathering data or samples that are easily accessible. While convenient, this approach has limitations as it can introduce bias, favoring certain outcomes. One significant drawback is that a convenience sample often fails to represent the entire population, potentially leading to systemic bias. Alternatively, systematic sampling could have been utilized. Systematic sampling is a more randomized approach where the researcher selects a starting point and collects every (n)-th data point from the population. This method is more likely to provide a representative sample of the entire population.
The collected data includes heights of individuals, with values ranging between 64 and 69 inches. The sample mean is 66.1 inches, and the sample standard deviation is 1.4491. Using the point estimate technique, which approximates population parameters (such as the mean) from random samples, the estimated mean of the data is also 66.1 inches (Encyclopedia Britannica, 2019).
For a 95% confidence interval, the calculated margin of error is 1.0366, resulting in a lower limit of 65.1 inches and an upper limit of 67.1 inches. The confidence interval provides a range within which the true population mean is likely to lie. Practically, this means that we can be 95% confident that the mean height of all individuals in the workplace falls between 65 and 67 inches.
To find a 99% confidence interval, the margin of error increases to 1.2927, resulting in a lower limit of 64.8 inches and an upper limit of 67.4 inches. The wider range reflects increased confidence in capturing the true population mean, although it also comes with a larger margin of error compared to the 95% interval. This indicates that as the confidence level increases, the interval becomes broader to ensure greater certainty that the true mean lies within the specified range.
Heading | Details | Analysis |
---|---|---|
Sampling Methods | – Convenience Sampling: Nonrandom, using readily available data; may introduce bias and fail to represent the population. – Systematic Sampling: Randomly selects a starting point and collects every (n)-th data point. | Systematic sampling offers better representation of the population, whereas convenience sampling is prone to systemic bias. |
Data Summary | – Sample Heights: 64, 65, 65, 65, 66, 66, 67, 67, 67, 69. – Sample Mean: 66.1 inches. – Sample Standard Deviation: 1.4491. – Point Estimate: 66.1 inches (Encyclopedia Britannica, 2019). | The point estimate provides a close approximation of the true population mean based on the given sample data. |
Confidence Intervals | – 95% Confidence Interval: Margin of error = 1.0366; Lower limit = 65.1 inches; Upper limit = 67.1 inches. – 99% Confidence Interval: Margin of error = 1.2927; Lower limit = 64.8 inches; Upper limit = 67.4 inches. | A 95% confidence interval is narrower but less certain, while a 99% confidence interval is wider with greater certainty of containing the true population mean. |
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