Theme Park Owner Wants To Know If The Children's Ride

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A theme park owner is interested in understanding whether 10-year-old girls and boys differ significantly in height, as this affects ride accessibility due to height restrictions. The owner collected height data for both groups, and the analysis aims to determine if there is a statistically significant difference in their heights at a 5% significance level. Additionally, the owner researched expected heights and standard deviations for children of this age, and this information is used to reassess the initial findings. The goal is to evaluate whether the two groups can be considered similar in height, thus allowing them equal access to rides, or if any differences could lead to disparate ride participation.

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Understanding the height differences between 10-year-old girls and boys is crucial for a theme park owner to ensure equitable access to rides that impose height restrictions. This analysis involves performing statistical tests to compare the means and variances of the two groups, thereby providing evidence to support or refute the hypothesis that the two groups differ significantly in height. The assessment proceeds in two parts: first, examining the raw data; second, incorporating external research findings to determine if the evidence aligns or diverges with initial results.

Initially, the data collected from the park's records indicated that the average heights for 10-year-old girls and boys were nearly identical, both averaging approximately 54.5 inches. To compare these groups, an independent two-sample t-test was employed, following an F-test for equality of variances. The F-test results suggested that the variances of the two groups were not significantly different at the 5% significance level, permitting the assumption of equal variances for the subsequent t-test.

The t-test results revealed a p-value greater than 0.05, which implies that there is insufficient evidence to reject the null hypothesis that the mean heights of girls and boys are equal. Consequently, based on the collected data, the conclusion is that there is no statistically significant difference in height between 10-year-old girls and boys in this sample. This result supports the premise that both groups are similarly capable height-wise to access the same rides, provided individual height restrictions are met.

However, the owner also researched official charts specifying expected heights and standard deviations for children at this age. According to these external sources, the mean height for 10-year-old girls and boys is 54.5 inches, with standard deviations of 2.74 inches for girls and 2.71 inches for boys. These figures are consistent with the data initially analyzed. Incorporating this information, the standard deviations suggest a similar variation within each group, reinforcing the assumption of comparable height distributions.

Furthermore, the external data supports that the initial conclusion — that there is no meaningful height difference between girls and boys — remains valid. Since the means are equal and the standard deviations are comparable, the probability that a randomly selected girl or boy would be significantly taller or shorter than the other is minimal. This outcome provides confidence that both groups can be considered similar in height, and thus, they can have equal opportunity to participate in rides without gender-based restrictions.

In conclusion, both the statistical analysis of the data collected and the external height information indicate that there is no significant height difference between 10-year-old girls and boys. As a result, the theme park can safely assume that both groups are equally eligible to access the same rides based on height restrictions, promoting fairness and equal enjoyment of the attractions. The park owner can utilize these findings to optimize ride accommodations and ensure equitable treatment for children, regardless of gender, at this age.

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