Problem 1

H0: R and X are equally likely Ha: R and X are not equally likely

P value: .01276 Level of Significance = .05 With a P value smaller than .05, the R and X are not equally likely. Reject the Null Hypothesis.

observed <- c(244, 192)

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

Problem 2

H0: There is no assosciation between Vitamin Use and Gender Ha: There is assosciation between Vitamin Use and Gender

P Value: .003944 Level of signficance: .05 Reject H0, the Null hypohtesis, we have enough to conclude there is an association between vitamin use and gender. .003944 < .05.

##         
##           No Occasional Regular
##   Female  87         77     109
##   Male    24          5      13
## 
##  Pearson's Chi-squared test
## 
## data:  vit_table
## X-squared = 11.071, df = 2, p-value = 0.003944

Problem 3

H0: All mean gill rates are = Ha: not all mean gill rates are =

P = .0121 Level of significance : .05 Reject H0, there is enough evidence to conclude that mean gill rate differs depending on the calcium level in the water.

##             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