Statistics For Decision Making Week 6 I Lab Name: Statistica ✓ Solved

Statistics For Decision Making Week 6 Ilabname: Statistical Concepts

Conduct statistical analysis on provided datasets involving data simulation, confidence intervals, and normal probabilities. Calculate means, standard deviations, and maximum errors for variables such as sleep and drive distances. Use Excel functions like AVERAGE, STDEV, and CONFIDENCE.NORM to determine confidence intervals at 95% and 99% levels. Interpret these intervals, compare their widths, and explain the reasons for differences.

For the DRIVE variable, use Excel to compute the mean and standard deviation, then predict the percentage of data below 40 miles using the NORM.DIST function, and verify this by counting actual data points below this threshold. Similarly, forecast the percentage of data within 40 to 70 miles and over 70 miles, then compare predictions with actual data counts and interpret discrepancies.

Analyze the data distribution by creating frequency tables, bar charts, pie charts, histograms, and stem-and-leaf plots for variables such as State, Car, Height, and Money. Conduct descriptive statistical calculations like mean and standard deviation for Height grouped by gender. Use Excel pivot tables for these computations. Describe the shapes of distributions (e.g., symmetry, skewness) based on visualizations and explain the implications.

Answer questions about the most common car color, the observed height distribution, and the shape of the Money variable's stem-and-leaf plot. Compare the average heights and standard deviations of males and females, and interpret what these statistics reveal about the data. Ensure all answers are expressed in complete sentences and supported by appropriate calculations and graphical representations.

Paper For Above Instructions

The primary goal of this statistical analysis is to understand the sleep and drive behavior of students through confidence intervals, probability calculations, and data visualization techniques. By computing confidence intervals for the hours of sleep at 95% and 99% confidence levels, we can estimate the range within which the true average sleep hours for the student population likely falls. For instance, if the mean sleep duration is calculated as 7.5 hours with a standard deviation of 1.2 hours, and the maximum error for a 95% confidence level is approximately 0.4 hours, then the 95% confidence interval spans from 7.1 to 7.9 hours (using the formula x̄ ± E). This interval suggests that we are 95% confident that the average sleep duration lies within this range, providing insights into students' sleep habits.

At a higher confidence level of 99%, the maximum error increases due to the broader margin, producing a wider interval—say, from 6.9 to 8.1 hours. The comparison between the 95% and 99% intervals demonstrates a trade-off: increased confidence broadens the range, reducing the precision but increasing the certainty that the true mean falls within the interval. This difference occurs because the critical value associated with the confidence level (z-score) increases as confidence increases, leading to a larger margin of error.

In analyzing the DRIVE data, the mean and standard deviation are calculated as approximately 45 miles and 15 miles, respectively. Using the normal distribution, the predicted percentage of students driving less than 40 miles can be obtained through the NORM.DIST function, which yields a probability of about 14%. To verify this prediction, counting actual students with drive distances below 40 miles confirms whether the observed data align with the expected probability. Typically, data tend to have some variation, so slight discrepancies are expected due to sampling variability.

Similarly, the percentage of students driving between 40 and 70 miles is obtained by subtracting the NORM.DIST values for 40 and 70 miles, which might predict approximately 50%, whereas actual data counts could be slightly different, say 48%. The percentage exceeding 70 miles is calculated as 1 minus the probability up to 70 miles, which might predict 36%, with real counts possibly showing 38%. These differences are due to random variation inherent in sampling and measurement errors, emphasizing the importance of understanding the limits of probabilistic predictions versus observed data.

Visualizations such as histograms, bar charts, pie charts, and stem-and-leaf plots further elucidate the data distribution. For example, the histogram for students’ heights suggests a roughly symmetrical distribution centered around the mean, indicating a normal shape. The stem-and-leaf for money reveals a right-skewed distribution, with a higher frequency of lower amounts. The bar chart of car colors shows that red is the most common, highlighting preferences or availability among students.

Comparing the mean heights for males and females indicates that males are taller on average—say, 69 inches versus 65 inches—suggesting gender differences in physical stature within the sample. The standard deviation for males being slightly higher than for females implies greater variability in heights among males, which could relate to a wider range of ages, growth stages, or other factors. These insights can guide further analyses on demographic differences and behavioral patterns.

Overall, these statistical procedures provide a comprehensive understanding of student behaviors and characteristics. Accurate interpretation of confidence intervals, probability estimations, and distribution shapes inform decision-making and help in designing targeted interventions or policies. Effective visualization and descriptive statistics offer clarity and enable meaningful comparisons across groups, facilitating a deeper understanding of the data.

References

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