Differences

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--- summary_of_hypothesis_testing:output01 [2025/11/30 15:31] – hkimscil
+++ summary_of_hypothesis_testing:output01 [2025/11/30 15:42] (current) – hkimscil
@@ Line 61: / Line 61: @@
 > diff <- m.treated.s-mean(p1)
 > diff/se.z1
-[1] 1.451929
+[1] 1.501677
 > zscore <- diff/se.z1
 > pnorm(zscore, lower.tail = F)*2
-[1] 0.1465213
+[1] 0.1331805
 > tscore <- zscore
 > pt(tscore, df=length(treated.s)-1, lower.tail = F)*2
-[1] 0.1554272
+[1] 0.1421495
 >
 > # usual way - using sample's variance
@@ Line 74: / Line 74: @@
 > se.s <- sqrt(var(treated.s)/n.s)
 > se.s
-[1] 1.549221
+[1] 1.599673
 > tscore <- diff/se.s
 > tscore
-[1] 1.562
+[1] 1.564567
 >
 >
@@ Line 110: / Line 110: @@
 > abline(v=m.treated.s, col='red', lwd=3)
 > se.s
-[1] 1.549221
+[1] 1.599673
 > se.z1
 [1] 1.666667
 >
 > c(m.treated.s-2*se.s, m.treated.s+2*se.s)
-[1]  99.32144 105.51832
+[1]  99.30345 105.70214
 > c <- qt(0.975, n.s-1)
 > c
 [1] 2.030108
 > c(m.treated.s-c*se.s, m.treated.s+c*se.s)
-[1]  99.2748 105.5650
+[1]  99.25529 105.75030
 > m.p2
 [1] 104
+>
+> x.p.est <- seq(m.treated.s-5*se.s,
++                m.treated.s+5*se.z1,
++                length.out = 500)
+> y.p.est <- dnorm(x.p.est, m.treated.s, se.s)
+>
+> plot(x.p.est, y.p.est, type = "l",
++      lwd=3,
++      main = "population mean estimated from a sample",
++      xlab = "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)
+> se3 <- c(m.treated.s-3*se.s, m.treated.s+3*se.s)
+> abline(v=c(m.treated.s,se1,se2,se3),
++        col=c('black', 'darkorange', 'darkorange',
++              'darkgreen', 'darkgreen',
++              'darkblue', 'darkblue'),
++        lwd=2)
+>
+>
 >
 >
 > pt(diff/se.s, df=n.s-1, lower.tail = F) * 2
-[1] 0.1272858
+[1] 0.1266823
 > t.test(treated.s, mu=m.p1, var.equal = T)
@@ Line 132: / Line 152: @@
 data:  treated.s
-t = 1.562, df = 35, p-value = 0.1273
+t = 1.5646, df = 35, p-value = 0.1267
 alternative hypothesis: true mean is not equal to 100
 percent confidence interval:
-.2748 105.5650
+.25529 105.75030
 sample estimates:
 mean of x
-.4199
+.5028
 >
 </code>
-{{.:pasted:20251130-153138.png}}
+{{.:pasted:20251130-154128.png}}
-{{.:pasted:20251130-153117.png}}
+{{.:pasted:20251130-154142.png}}
+{{.:pasted:20251130-154159.png}}