title: “ACTN3, Nutrition, and Fish Gill Analysis” author: “Gerney Johnson” date: “2026-04-26” output: html_document
knitr::opts_chunk$set(echo = TRUE, warning = FALSE, message = FALSE) library(tidyverse)
Problem 1: ACTN3 Allele Distribution
Hypotheses:
\(H_0\): The alleles R and X are equally likely (\(P_R = 0.5, P_X = 0.5\)).
\(H_a\): The alleles R and X are not equally likely.
actn3_counts <- c(244, 192) chisq.test(actn3_counts, p = c(0.5, 0.5))
Conclusion: The p-value is 0.0126. Since this is less than 0.05, we reject the null hypothesis. There is significant evidence that the alleles are not equally likely.
Problem 2: Vitamin Use and Gender
Hypotheses:
\(H_0\): Gender and Vitamin Use are independent (no association).
\(H_a\): There is a significant association between Gender and Vitamin Use.
vit_table <- table(NutritionStudy\(Gender, NutritionStudy\)VitaminUse) chisq.test(vit_table)
Conclusion: The p-value is 0.003944. Since the p-value is less than 0.05, we reject the null hypothesis. There is a statistically significant association between gender and vitamin use.
Problem 3: Calcium Levels and Fish Gill Rates
Hypotheses:
\(H_0\): The mean gill rates are equal across all calcium levels (\(\mu_{low} = \mu_{med} = \mu_{high}\)).
\(H_a\): At least one mean gill rate is significantly different.
gill_anova <- aov(GillRate ~ as.factor(Calcium), data = FishGills3) summary(gill_anova)
Conclusion: The p-value is < 0.001. Since the p-value is less than 0.05, we reject the null hypothesis. We conclude that the calcium level of the water has a significant effect on the fish’s respiration rate.