Statistics 1: Confidence Intervals and Basketball Players' Height

This assignment focuses on the concept of confidence intervals in statistics, using the example of basketball players' heights. It explains how to calculate the confidence interval, the impact of sample size on the standard error, and the relationship between the confidence level and the margin of error. The solution demonstrates how the sample size influences the width of the confidence interval and how a higher confidence level affects the margin of error. The assignment highlights the practical application of these statistical concepts, providing a clear understanding of how to interpret and apply confidence intervals in real-world scenarios. The student provides a detailed analysis of the given data and explains the underlying statistical principles.

Running header: PSY87540 Statistics 1
PSY87540 Statistics
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PSY87540 Statistics 2
1. A random sample of 25 professional basketball players shows a mean height of 6 feet, 5
inches with a 95% confidence interval of 0.4 inches. Explain what this indicates.
The above information indicates that the average height of the 25 basketball players is 6
feet, 5 inches. Moreover, the margin of error for the sample is 0.4 inches. Therefore, the
population mean of profession basketball players will lie between 6 feet 4.6 inches and 6 feet,
5.4 inches. The above limits are calculated using the following formula;
Confidence Interval=mean ±margin of error
Confidence Interval=6 feet ,5 inches ± 0.4 inches
Lower limit =6 feet 4.6 inches
Upper Limit=6 feet 5.4 inches
2. If the sample were smaller, would the confidence interval become smaller or larger?
Explain
Notably, one of the measurements used in calculating the confidence interval is the
standard error (Standard error = σ/n) n is the sample size. Increasing the sample size decreases
the standard error thus decreases the width of confidence intervals, because it. Therefore, if the
sample size was smaller the confidence interval would become larger.
3. If you wanted a higher level of confidence (99%) would the confidence interval become
smaller or larger? Explain.
Notably, one of the measurements used in calculating the confidence interval is the
critical value (Z), the higher the confidence level the higher the Z value. The increase in the level
of confidence leads to an increase in the margin of error, which results in a increase in the
confidence level. Therefore, by using 99% confidence level would make the confidence interval
become larger.