Differences

This shows you the differences between two versions of the page.

--- b:head_first_statistics:constructing_confidence_intervals [2019/12/03 14:08] – [Just one more problem...] hkimscil
+++ b:head_first_statistics:constructing_confidence_intervals [2019/12/05 13:46] – [Four steps for finding confidence intervals] hkimscil
@@ Line 10: / Line 10: @@
 Rather than specify an exact value, we can specify two values we expect flavor duration to lie between.
-{{:b:head_first_statistics:pasted:20191203-121916.png}}
+[{{:b:head_first_statistics:pasted:20191203-121916.png  }}] : As an example, you may want to choose a and b so that there’s a 95% chance of the interval containing the population mean. Finding the exact spot of a and b is the problem we are trying to solve.
-The far side of each end, (a, b) is called a confidence interval.
+The far side of each end, (a, b) is called a **//confidence interval//**.
-{{:b:head_first_statistics:pasted:20191203-122050.png}}
 ===== Four steps for finding confidence intervals =====
-Step 1: Choose your population statistic
+{{:b:head_first_statistics:pasted:20191203-122050.png}}
-Step 2: Find its sampling distribution
-[{{:b:head_first_statistics:pasted:20191203-122301.png}}]{{:b:head_first_statistics:pasted:20191203-122550.png}}
+<fs large>**Step 1:**</fs> Choose your population statistic
-Mighty Gumball used a sample of 100 gumballs to come up with their
+If we go back to the work we did in the last chapter, then the sampling distribution of means has the following expectation and variance:
-estimates, and they have calculated that s2 = 25. This means that
+{{:b:head_first_statistics:pasted:20191203-122301.png}}
+<fs large>**Step 2**</fs>: Find its __**sampling distribution**__
+샘플평균들의 분산은 ($Var(\overline{X})$) 모집단의 특성인데 (parameter), 이를 알 수는 없으므로 아래와 같이 샘플의 분산값을 ($s^{2}$) 사용하여 샘플평균들의 분포를 만든다.
+{{:b:head_first_statistics:pasted:20191203-122550.png}}
+Mighty Gumball used a sample of 100 gumballs to come up with their estimates, and they have calculated that s<sup>2</sup> = 25. This means that
 {{:b:head_first_statistics:pasted:20191203-122843.png}}
 {{:b:head_first_statistics:pasted:20191203-122946.png}}
-Step 3: Decide on the level of confidence
+<fs large>**Step 3:**</fs> Decide on the level of confidence
-Step 4: Find the confidence limits
+<fs large>**Step 4:**</fs> Find the confidence limits
 {{:b:head_first_statistics:pasted:20191203-123220.png}}
@@ Line 98: / Line 106: @@
 ====== Just one more problem... ======
-Step 1: Choose your population statistic
+==== Step 1: Choose your population statistic ====
 Mighty Gumball has taken a representative sample of 10 gumballs and weighed each one. In their sample, x = 0.5 oz and s<sup>2</sup> = 0.09.
-Step 2: Find its sampling distribution
+==== Step 2: Find its sampling distribution ====
 The normal distribution isn't a good approximation for every situation.
@@ Line 119: / Line 125: @@
 {{:b:head_first_statistics:pasted:20191203-133508.png}}
-Step 3: Decide on the level of confidence
+==== Step 3: Decide on the level of confidence ====
 {{:b:head_first_statistics:pasted:20191203-133812.png}}
-Step 4: Find the confidence limits
+==== Step 4: Find the confidence limits ====
 {{:b:head_first_statistics:pasted:20191203-133742.png}}
+===== The t-distribution vs. the normal distribution =====
 {{:b:head_first_statistics:pasted:20191203-133845.png}}