Theme Park Owner Wants To Know If The Childrens Rides Are Fav A theme park owner wants to know if the children’s rides are favoring 10-year-old girls over 10-year-old boys based on height. Specifically, the owner is interested in whether there is a significant difference in the heights of these two groups, as the ability to ride certain attractions is determined by height thresholds. The owner has gathered height data on 10-year-old girls and boys, and the task is to analyze this data to determine if the two groups have statistically different mean heights at the 5% significance level. Additionally, the owner has found population data indicating that both girls and boys have an average height of 54.5 inches with standard deviations of approximately 2.74 inches for girls and 2.71 inches for boys. The question is whether incorporating this external population information alters the conclusion from the initial data analysis. The owner seeks a comprehensive interpretation of the statistical tests, including assumptions, calculations, and conclusions, all in the context of the amusement park setting.
Paper For Above instruction In this analysis, we investigate whether there is a statistically significant difference in the heights of 10-year-old girls and boys, which may influence their eligibility to access certain rides in a theme park. The core aim is to determine if gender-based height differences exist, using hypothesis testing methods suitable for comparing two independent groups. Part A: Hypothesis Testing Based on Sample Data First, we set up the null hypothesis (H■) that there is no difference between the mean heights of girls and boys, i.e., H■: µ_girls = µ_boys. The alternative hypothesis (H■) is that there is a difference, H■: µ_girls ≠ µ_boys. Given the nature of the data and the aim of detecting any difference, a two-tailed test is appropriate at the 5% significance level (α = 0.05). The data collected from the sample indicate the following: the sample means for girls and boys, their sample variances, and sample sizes. Suppose the sample mean heights for girls and boys are both approximately 54 inches, with sample variances near 6.9 for girls and 50.9 for boys, and the sample sizes are around 20 observations for each group. Before conducting the t-test for comparing the means, we should assess whether the variances of the two groups are equal. An F-test for equality of variances is performed. The F-statistic is calculated as the ratio of the larger variance to the smaller variance. Here, F = 50.9 / 6.9 ≈ 7.38. Comparing this to the critical