Add A1

.gitignore

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+.Rproj.user
+.Rhistory
+.RData
+.Ruserdata
+
+# Generated Documents
+*.html
+*.pdf

A1.Rmd

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+---
+title: "Assignment 1"
+subtitle: "STAT3373"
+author: "Isaac Shoebottom"
+date: "Sept 18th, 2025"
+output:
+  pdf_document: default
+  html_document:
+    df_print: paged
+---
+
+# Question 1
+
+## a)
+
+```{r}
+data <- c(14.2, 16.1, 15.8, 17.2, 14.5, 15.3, 16.8, 15.9, 14.7, 16.4, 15.1, 17.5, 15.6, 16.2, 14.9, 15.7, 16.9, 15.4, 16.6, 15.2)
+```
+
+$$ H_0 : \mu = 15, \space H_\alpha : \mu \neq 15 $$ $$ n = 20, \space \alpha = 0.05, \space \bar{x}=15.8$$
+
+```{r}
+(mean(data) - 15)/(sd(data)/sqrt(20)) # t-value
+qt(1 - (0.05/2), 20-1) # critical t-value
+
+```
+
+Because t is greater than the critical t, 3.910959 \> 2.093024, we can reject the null hypothesis. The medicine does not take effect in 15 minutes
+
+## b)
+
+```{r}
+qt(1 - (0.05/2), 20-1) * (sd(data)/sqrt(20)) # Interval from mean
+mean(data) - qt(1 - (0.05/2), 20-1) * (sd(data)/sqrt(20))
+mean(data) + qt(1 - (0.05/2), 20-1) * (sd(data)/sqrt(20))
+```
+
+The confidence interval with 95% confidence is [15.37186, 16.22814]
+
+# Question 2
+
+## a)
+
+```{r}
+before <- c(72, 68, 75, 81, 69, 73, 77, 70, 74, 79)
+after <- c(78, 71, 80, 85, 76, 75, 82, 76, 79, 84)
+diff <- after - before
+```
+
+$$ H_0 : \mu \leq 0, \space H_\alpha : \mu > 0$$ $$ n = 10, \space \alpha = 0.01, \space \bar{d}=4.8$$
+
+```{r}
+mean(diff)/(sd(diff)/sqrt(10)) # t-value
+qt(1 - (0.01/2), 10 - 1) # critical t-value
+```
+
+Because t is greater than critical t, 10.28571 \> 3.249836, we can reject the null hypothesis. The method does improve test scores
+
+## b)
+
+```{r}
+qt(1 - (0.01/2), 10-1) * (sd(diff)/sqrt(10)) # Interval from mean
+mean(diff) - qt(1 - (0.01/2), 10-1) * (sd(diff)/sqrt(10))
+mean(diff) + qt(1 - (0.01/2), 10-1) * (sd(diff)/sqrt(10))
+```
+
+The confidence interval with 99% confidence is [3.28341, 6.31659]

STAT6473.Rproj

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