hw 8 data 101

Author

kenneth 

setwd("~/Data 101")
fish <- read.csv("FishGills3.csv")
nutritions <- 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.

Ho: p1= p2 = 1/2

Ha:at least one pi ≠ 1/3

observed <- c(244,192)

theoretical_prop <- rep(1/2, 2)

counts

expected_values <- theoretical_prop*sum(observed) 
expected_values
[1] 218 218
chisq.test(observed)

    Chi-squared test for given probabilities

data:  observed
X-squared = 6.2018, df = 1, p-value = 0.01276

The p-value is 0.01276, which is less than 0.05 so we will reject the null. There is strong evidence showing at least one proportion is not equal to 1/2.

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)

head(nutritions)
  ID Age Smoke Quetelet Vitamin Calories  Fat Fiber Alcohol Cholesterol
1  1  64    No  21.4838       1   1298.8 57.0   6.3     0.0       170.3
2  2  76    No  23.8763       1   1032.5 50.1  15.8     0.0        75.8
3  3  38    No  20.0108       2   2372.3 83.6  19.1    14.1       257.9
4  4  40    No  25.1406       3   2449.5 97.5  26.5     0.5       332.6
5  5  72    No  20.9850       1   1952.1 82.6  16.2     0.0       170.8
6  6  40    No  27.5214       3   1366.9 56.0   9.6     1.3       154.6
  BetaDiet RetinolDiet BetaPlasma RetinolPlasma    Sex VitaminUse PriorSmoke
1     1945         890        200           915 Female    Regular          2
2     2653         451        124           727 Female    Regular          1
3     6321         660        328           721 Female Occasional          2
4     1061         864        153           615 Female         No          2
5     2863        1209         92           799 Female    Regular          1
6     1729        1439        148           654 Female         No          2
summary(nutritions)
       ID             Age           Smoke              Quetelet    
 Min.   :  1.0   Min.   :19.00   Length:315         Min.   :16.33  
 1st Qu.: 79.5   1st Qu.:39.00   Class :character   1st Qu.:21.80  
 Median :158.0   Median :48.00   Mode  :character   Median :24.74  
 Mean   :158.0   Mean   :50.15                      Mean   :26.16  
 3rd Qu.:236.5   3rd Qu.:62.50                      3rd Qu.:28.85  
 Max.   :315.0   Max.   :83.00                      Max.   :50.40  
    Vitamin         Calories           Fat             Fiber      
 Min.   :1.000   Min.   : 445.2   Min.   : 14.40   Min.   : 3.10  
 1st Qu.:1.000   1st Qu.:1338.0   1st Qu.: 53.95   1st Qu.: 9.15  
 Median :2.000   Median :1666.8   Median : 72.90   Median :12.10  
 Mean   :1.965   Mean   :1796.7   Mean   : 77.03   Mean   :12.79  
 3rd Qu.:3.000   3rd Qu.:2100.4   3rd Qu.: 95.25   3rd Qu.:15.60  
 Max.   :3.000   Max.   :6662.2   Max.   :235.90   Max.   :36.80  
    Alcohol         Cholesterol       BetaDiet     RetinolDiet    
 Min.   :  0.000   Min.   : 37.7   Min.   : 214   Min.   :  30.0  
 1st Qu.:  0.000   1st Qu.:155.0   1st Qu.:1116   1st Qu.: 480.0  
 Median :  0.300   Median :206.3   Median :1802   Median : 707.0  
 Mean   :  3.279   Mean   :242.5   Mean   :2186   Mean   : 832.7  
 3rd Qu.:  3.200   3rd Qu.:308.9   3rd Qu.:2836   3rd Qu.:1037.0  
 Max.   :203.000   Max.   :900.7   Max.   :9642   Max.   :6901.0  
   BetaPlasma     RetinolPlasma        Sex             VitaminUse       
 Min.   :   0.0   Min.   : 179.0   Length:315         Length:315        
 1st Qu.:  90.0   1st Qu.: 466.0   Class :character   Class :character  
 Median : 140.0   Median : 566.0   Mode  :character   Mode  :character  
 Mean   : 189.9   Mean   : 602.8                                        
 3rd Qu.: 230.0   3rd Qu.: 716.0                                        
 Max.   :1415.0   Max.   :1727.0                                        
   PriorSmoke   
 Min.   :1.000  
 1st Qu.:1.000  
 Median :2.000  
 Mean   :1.638  
 3rd Qu.:2.000  
 Max.   :3.000

Ho = There is no association between gender and vitamin use Ha = There is a association between gender and vitamin use

observed_dataset <- table(nutritions$VitaminUse, nutritions$Sex)
observed_dataset
            
             Female Male
  No             87   24
  Occasional     77    5
  Regular       109   13
chisq.test(observed_dataset)

    Pearson's Chi-squared test

data:  observed_dataset
X-squared = 11.071, df = 2, p-value = 0.003944

Because the p-value is .003944 which is less than .05 so we will reject the null.There is strong evidence that there is a association between gender and vitamin use.

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. μ1=is low calcium levels μ2=is medium calcium levels μ3=is high calcium levels

Ho: μ1= μ2 = μ2

ha= one μ is different from the others

head(fish)
  Calcium GillRate
1     Low       55
2     Low       63
3     Low       78
4     Low       85
5     Low       65
6     Low       98
summary(fish)
   Calcium             GillRate    
 Length:90          Min.   :33.00  
 Class :character   1st Qu.:48.00  
 Mode  :character   Median :62.50  
                    Mean   :61.78  
                    3rd Qu.:72.00  
                    Max.   :98.00  
anova_answer <- aov(GillRate ~ Calcium, data = fish)

anova_answer
Call:
   aov(formula = GillRate ~ Calcium, data = fish)

Terms:
                  Calcium Residuals
Sum of Squares   2037.222 19064.333
Deg. of Freedom         2        87

Residual standard error: 14.80305
Estimated effects may be unbalanced
summary(anova_answer)
            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

Because the p-value is .0121, we will reject the null. There is very strong evidence to suggests that at least one of the calcium levels is different from the other calcium levels.