Differences

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--- summary_of_hypothesis_testing:output01 [2025/11/30 15:42] – hkimscil
+++ summary_of_hypothesis_testing:output01 [2025/11/30 22:50] (current) – hkimscil
@@ Line 17: / Line 17: @@
 > sd.p2 <- sd(p2)
 >
-> n.s <- 36
+> n.s <- 25
 > se.z1 <- c(sqrt(var(p1)/n.s))
 > se.z2 <- c(sqrt(var(p2)/n.s))
 > se.z1
-[1] 1.666667
+[1] 2
 > se.z2
-[1] 1.666667
+[1] 2
 >
 > x.p1 <- seq(mean(p1)-5*se.z1,
@@ Line 40: / Line 40: @@
 > plot(x.p1, y.p1, type = "l",
 +      lwd=3,
-+      main = "Sample means from p1 and p2 (imaginary)",
++      main = paste0("sample (n = ",n.s, ") means from p1 and p2 (unknown)"),
 +      xlab = "Value", ylab = "Density")
 > lines(x.p2, y.p2, lty=2, lwd=3)
@@ Line 61: / Line 61: @@
 > diff <- m.treated.s-mean(p1)
 > diff/se.z1
-[1] 1.501677
+[1] 0.5253907
-> zscore <- diff/se.z1
+> zscore <- abs(diff/se.z1)
 > pnorm(zscore, lower.tail = F)*2
-[1] 0.1331805
+[1] 0.5993116
 > tscore <- zscore
-> pt(tscore, df=length(treated.s)-1, lower.tail = F)*2
+> pt(tscore, df=n.s-1, lower.tail = F)*2
-[1] 0.1421495
+[1] 0.6041323
 >
 > # usual way - using sample's variance
@@ Line 74: / Line 74: @@
 > se.s <- sqrt(var(treated.s)/n.s)
 > se.s
-[1] 1.599673
+[1] 1.83652
 > tscore <- diff/se.s
 > tscore
-[1] 1.564567
+[1] 0.572159
 >
 >
@@ Line 110: / Line 110: @@
 > abline(v=m.treated.s, col='red', lwd=3)
 > se.s
-[1] 1.599673
+[1] 1.83652
 > se.z1
-[1] 1.666667
+[1] 2
 >
 > c(m.treated.s-2*se.s, m.treated.s+2*se.s)
-[1]  99.30345 105.70214
+[1]  97.37774 104.72382
 > c <- qt(0.975, n.s-1)
 > c
-[1] 2.030108
+[1] 2.063899
 > c(m.treated.s-c*se.s, m.treated.s+c*se.s)
-[1]  99.25529 105.75030
+[1]  97.26039 104.84117
 > m.p2
 [1] 104
@@ Line 131: / Line 131: @@
 > plot(x.p.est, y.p.est, type = "l",
 +      lwd=3,
-+      main = "population mean estimated from a sample",
++      main = paste0("mu (", m.p2, ") estimation \n", "from a sample ", "mean=", round(m.treated.s,2)),
-+      xlab = "Value", ylab = "Density")
++      xlab = paste0("Value"), ylab = "Density")
 > se1 <- c(m.treated.s-se.s, m.treated.s+se.s)
 > se2 <- c(m.treated.s-2*se.s, m.treated.s+2*se.s)
@@ Line 142: / Line 142: @@
 +        lwd=2)
 >
->
+> tscore <- abs(diff/se.s)
->
+> pt(tscore, df=n.s-1, lower.tail = F) * 2
->
+[1] 0.5725352
-> pt(diff/se.s, df=n.s-1, lower.tail = F) * 2
-[1] 0.1266823
 > t.test(treated.s, mu=m.p1, var.equal = T)
@@ Line 152: / Line 150: @@
 data:  treated.s
-t = 1.5646, df = 35, p-value = 0.1267
+t = 0.57216, df = 24, p-value = 0.5725
 alternative hypothesis: true mean is not equal to 100
 percent confidence interval:
-.25529 105.75030
+.26039 104.84117
 sample estimates:
 mean of x
-.5028
+.0508
 >
 </code>
-{{.:pasted:20251130-154128.png}}
+{{.:pasted:20251130-225009.png}}
-{{.:pasted:20251130-154142.png}}
+{{.:pasted:20251130-225016.png}}
-{{.:pasted:20251130-154159.png}}
+{{.:pasted:20251130-225024.png}}