library(readr)
# Problem 1
obs <- c(R = 244, X = 192)
exp <- c(436/2, 436/2)

chisq.test(x = obs, p = c(0.5, 0.5))
## 
##  Chi-squared test for given probabilities
## 
## data:  obs
## X-squared = 6.2018, df = 1, p-value = 0.01276

Hypotheses

H0: R and X alleles are equally likely (pR = pX).

HA: R and X alleles are not equally likely.

Conclusion

Because p = 0.0128 < 0.05, we reject the null hypothesis. There is evidence that the two alleles are not equally likely in the population.

# Problem 2
data <- read.csv("NutritionStudy.csv")

tbl <- table(data$VitaminUse, data$Sex)
chisq.test(tbl)
## 
##  Pearson's Chi-squared test
## 
## data:  tbl
## X-squared = 11.071, df = 2, p-value = 0.003944

Hypotheses

H0: Vitamin use and gender are independent.

HA: Vitamin use and gender are associated.

Conclusion

Because p = 0.00394 < 0.05, we reject H0. There is a significant association between gender and vitamin use.

# Problem 3
fish <- read.csv("FishGills3.csv")

model <- aov(GillRate ~ Calcium, data = fish)
summary(model)
##             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 ' ' 1

Hypotheses

H0: Mean gill rate is the same across all calcium levels.

HA: At least one calcium level has a different mean gill rate.

Conclusion

Because p = 0.0121 < 0.05, we reject H0. Mean gill rate differs significantly among calcium levels.