| title:“HW 8” |
| author:“Victoria” |
| date:“2025-11-22” |
| output:html_document |
#Observed counts
observed <- c(R = 244, X = 192)
# Null values
theoritical_prop <- c(0.5,0.5)Hypothesis:
\(H_0\):\(p_R\) = \(p_X\)= 0.5 \(H_a\):\(p_R\) different from \(p_X\)
# Expected values
expected_values <- theoritical_prop*sum(observed)
expected_values## [1] 218 218# Perform chi-squared goodness-of-fit test
chisq.test(observed)##
## Chi-squared test for given probabilities
##
## data: observed
## X-squared = 6.2018, df = 1, p-value = 0.01276Results: p-value = 0.01276
Conclusion: Because the p-value is less than the standard significance level of 0.05, we reject the null hypothesis. There is significant evidence that R and X are not equally likely in the population.
library(tidyverse)## Warning: package 'readr' was built under R version 4.5.2## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.6
## ✔ forcats 1.0.1 ✔ stringr 1.5.2
## ✔ ggplot2 4.0.0 ✔ tibble 3.3.0
## ✔ lubridate 1.9.4 ✔ tidyr 1.3.1
## ✔ purrr 1.1.0
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorsNutritionStudy <- 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.summary(NutritionStudy)## 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. :3.000Hypothesis: Ho: Vitamin use is associated with sex Ha: Vitamin use is not associated with sex
observed_dataset<- table(NutritionStudy$VitaminUse, NutritionStudy$Sex)
observed_dataset##
## Female Male
## No 87 24
## Occasional 77 5
## Regular 109 13chisq.test(observed_dataset)##
## Pearson's Chi-squared test
##
## data: observed_dataset
## X-squared = 11.071, df = 2, p-value = 0.003944Results: p-value = 0.003944 Conclusion: Because the p-value is less than the standard significance value of 0.05 we reject the null hypothesis and there is significant evidence that there is an association between Vitamin use and sex.
library(tidyverse)
FishGills3<- 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.head(FishGills3)## # A tibble: 6 × 2
## Calcium GillRate
## <chr> <dbl>
## 1 Low 55
## 2 Low 63
## 3 Low 78
## 4 Low 85
## 5 Low 65
## 6 Low 98Hypothesis: \(H_0\): \(\mu_low\) = \(\mu_medium\) = \(\mu_high\) \(H_a\): at least one calcium level has a mean gill beat rate that differs from the others
# Perform ANOVA
anova_result <- aov(GillRate ~ Calcium, data = FishGills3)
anova_result## Call:
## aov(formula = GillRate ~ Calcium, data = FishGills3)
##
## 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 ' ' 1Results: p-value = 0.121 Conclusion: The p-value is small, indicating strong evidence against the null hypothesis. Overall, this test suggests thatat least one calcium level has a mean gill beat rate that differs from the others.