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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorssetwd("~/Documents/EC/Spring 2026/DATA 101")
fish_gills <- read_csv("FishGills3.csv")## Rows: 90 Columns: 2
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): Calcium
## dbl (1): GillRate
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.nutrition <- read_csv("NutritionStudy.csv")## Rows: 315 Columns: 17
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (3): Smoke, Sex, VitaminUse
## dbl (14): ID, Age, Quetelet, Vitamin, Calories, Fat, Fiber, Alcohol, Cholest...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.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.
p1: Proportion of people classified as R p2: Proportion of people classified as X
H0: p1 = p2 = 1/2 Ha: At least one p≠1/2
ACTN3 <- c(244, 192)
theoritical_prop <- rep(1/2, 2)expected_values <- theoritical_prop*sum(ACTN3)
expected_values## [1] 218 218All values are above 5, we can continue with the chi-squared test.
chisq.test(ACTN3)##
## Chi-squared test for given probabilities
##
## data: ACTN3
## X-squared = 6.2018, df = 1, p-value = 0.01276p-value: 0.01276
With a p-value less than 0.05, we reject the null, the ACTN3 genetic alleles R and X are not equally likely.
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)
H0: There is not significant association between information about vitamin use and the gender of participants. Ha: There is significant association between information about vitamin use and the gender of participants.
observed_dataset <- table(nutrition$VitaminUse, nutrition$Sex)
observed_dataset##
## Female Male
## No 87 24
## Occasional 77 5
## Regular 109 13chisq.test(nutrition$VitaminUse, nutrition$Sex)$expected## nutrition$Sex
## nutrition$VitaminUse Female Male
## No 96.20000 14.80000
## Occasional 71.06667 10.93333
## Regular 105.73333 16.26667All values are above 5, we can continue with the chi-squared test.
chisq.test(observed_dataset)##
## Pearson's Chi-squared test
##
## data: observed_dataset
## X-squared = 11.071, df = 2, p-value = 0.003944p-value: 0.003944
With a p-value less than 0.05, we reject the null, there is significant association between information about vitamin use and the gender of participants.
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.
μ1 = Low calcium level mean gill rate μ2 = Medium calcium level mean gill rate μ3 = High calcium level mean gill rate
H0: μ1 = μ2 = μ3 Ha: At least one μ is different from the others
anova_result <- aov(GillRate ~ Calcium, data = fish_gills)
anova_result## Call:
## aov(formula = GillRate ~ Calcium, data = fish_gills)
##
## Terms:
## Calcium Residuals
## Sum of Squares 2037.222 19064.333
## Deg. of Freedom 2 87
##
## Residual standard error: 14.80305
## Estimated effects may be unbalancedsummary(anova_result)## 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
With a p-value less than 0.05, we reject the null, we can conclude that at least one of the mean gill rates differs depending on the calcium level.