setwd("C:/Users/COCO3/Downloads")
Fishdata <- read.csv("FishGills3.csv")
Nutritiondata <- read.csv("NutritionStudy.csv")Problem 1: ACTN3 is a gene that encodes alpha-actinin-3, a protein in fast-twitch muscle fibers, important for activities like sprinting and weightlifting. The gene has two main alleles: R (functional) and X (non-functional). The R allele is linked to better performance in strength, speed, and power sports, while the X allele is associated with endurance due to a greater reliance on slow-twitch fibers. However, athletic performance is influenced by various factors, including training, environment, and other genes, making the ACTN3 genotype just one contributing factor. A study examines the ACTN3 genetic alleles R and X, also associated with fast-twitch muscles. Of the 436 people in this sample, 244 were classified as R, and 192 were classified as X. Does the sample provide evidence that the two options are not equally likely? Conduct the test using a chi-square goodness-of-fit test
observed <- c (244,192)
theoretical_prop <- rep (1/2,2)
expected_values <- theoretical_prop*sum(observed)
expected_values## [1] 218 218chisq.test(observed)##
## Chi-squared test for given probabilities
##
## data: observed
## X-squared = 6.2018, df = 1, p-value = 0.01276#Hypotheses: \(H_0\)= R and X alleles are each 50% likely \(H_a\)= R and X alleles are not each 50% likely
P-value = 0.0128
Problem 2: Who Is More Likely to Take Vitamins: Males or Females? The dataset NutritionStudy contains, among other things, information about vitamin use and the gender of the participants. Is there a significant association between these two variables? Use the variables VitaminUse and Gender to conduct a chi-square analysis and give the results. (Test for Association)
new_table <- table(Nutritiondata$Sex,Nutritiondata$VitaminUse)
new_table##
## No Occasional Regular
## Female 87 77 109
## Male 24 5 13##Hypotheses \(H_0\)= No association between gender and vitamin use \(H_a\)= There is an association between gender and vitamin use
#Check if you can do the test
chisq.test(new_table)$expected##
## No Occasional Regular
## Female 96.2 71.06667 105.73333
## Male 14.8 10.93333 16.26667#Actually do the test
chisq.test(new_table)##
## Pearson's Chi-squared test
##
## data: new_table
## X-squared = 11.071, df = 2, p-value = 0.003944P value= 0.003944
Problem 3: Most fish use gills for respiration in water, and researchers can observe how fast a fish’s gill cover beats to study ventilation, much like we might observe a person’s breathing rate. Professor Brad Baldwin is interested in how water chemistry might affect gill beat rates. In one experiment, he randomly assigned fish to tanks with different calcium levels. One tank was low in calcium (0.71 mg/L), the second tank had a medium amount (5.24 mg/L), and the third tank had water with a high calcium level (18.24 mg/L). His research team counted gill rates (beats per minute) for samples of 30 fish in each tank. The results are stored in FishGills3. Perform ANOVA test to see if the mean gill rate differs depending on the calcium level of the water
#Hypotheses \(H_0\)= The mean gill rate is the same for all levels of calcium \(H_a\)= There is one or more calcium level that has a different mean gill rate #Anova test
anova_test <- aov (GillRate ~ Calcium, data = Fishdata)
summary (anova_test)## Df Sum Sq Mean Sq F value Pr(>F)
## Calcium 2 2037 1018.6 4.648 0.0121 *
## Residuals 87 19064 219.1
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1P value = 0.0121
#Conclusion: The p value is less that 0.05, so we reject the null. There is enough evidence to say the mean gill rate changes based on calcium levels of the water