Week11 practice 2 - ประวัติรุ่นแก้ไข

Jittat: /* Confidence intervals, known variance \sigma^2 */

2014-11-06T02:08:12Z

Confidence intervals, known variance \sigma^2

2014-11-06T02:06:08Z

Confidence intervals, known variance \sigma^2

2014-11-06T02:05:03Z

Confidence intervals, known variance \sigma^2

2014-11-06T02:01:13Z

2014-11-06T02:00:53Z

Confidence interval, known \sigma

2014-11-06T01:54:38Z

Sampling and statistics

2014-11-06T01:50:55Z

Sampling and statistics

2014-11-06T01:45:53Z

Sampling and statistics

2014-11-06T01:45:40Z

Sampling and statistics

2014-11-06T01:40:46Z

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 02:08, 6 พฤศจิกายน 2557
แถว 20:		แถว 20:
	For each of the data set, ask your friend for the real <math>\sigma</math>.		For each of the data set, ask your friend for the real <math>\sigma</math>.

−	~~Recall that~~ the ~~random variable <math>\bar{X}</math> is a normal random variable with mean <math>\mu</math> and s.d. <math>\sigma/\sqrt{n}</math> Therefore~~,	+	For each of the data set, compute the confidence interval for the levels of confidence of 80%, 90%, 95%, and 99%.
−
−	~~<center>~~
−	~~<math>\sqrt{n}(\bar{X}-\mu)/\sigma</math>~~
−	~~</center>~~
−
−	~~will be a unit normal random variable.~~
−
−	~~We consider how <math>\bar{X}</math> deviates from~~ the ~~true mean <math>\mu</math>~~.

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 02:06, 6 พฤศจิกายน 2557
แถว 27:		แถว 27:

	will be a unit normal random variable.		will be a unit normal random variable.
		+
		+	We consider how <math>\bar{X}</math> deviates from the true mean <math>\mu</math>.

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 02:05, 6 พฤศจิกายน 2557
แถว 18:		แถว 18:

	== Confidence intervals, known variance <math>\sigma^2</math> ==		== Confidence intervals, known variance <math>\sigma^2</math> ==
		+	For each of the data set, ask your friend for the real <math>\sigma</math>.
		+
		+	Recall that the random variable <math>\bar{X}</math> is a normal random variable with mean <math>\mu</math> and s.d. <math>\sigma/\sqrt{n}</math> Therefore,
		+
		+	<center>
		+	<math>\sqrt{n}(\bar{X}-\mu)/\sigma</math>
		+	</center>
		+
		+	will be a unit normal random variable.

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 02:01, 6 พฤศจิกายน 2557
แถว 18:		แถว 18:

	== Confidence intervals, known variance <math>\sigma^2</math> ==		== Confidence intervals, known variance <math>\sigma^2</math> ==
−
−	~~== Confidence interval, unknown <math>\sigma</math> ==~~

@@ แถว 17: / แถว 17: @@
 Compare your estimates of means and s.d. with the actual values from your generator.
-== Confidence interval, known <math>\sigma</math> ==
+== Confidence intervals, known variance <math>\sigma^2</math> ==
 == Confidence interval, unknown <math>\sigma</math> ==

@@ แถว 8: / แถว 8: @@
 Generate 10 sets of data:
-* For a normal distribution (with different parameters), generate samples of size <math>n = 5, 10, 50, 100, 500</math>.  We shall call these sets of data set 1, set 2,..., and set 5.
+* For normal distributions (with different parameters), generate samples of size <math>n = 5, 10, 50, 100, 500</math>.  We shall call these sets of data set 1, set 2,..., and set 5.
-* For a uniform distribution (with different parameters), generate samples of size <math>n = 5, 10, 50, 100, 500</math>.  We shall call these sets of data set 6, set 7, ..., and set 10.
+* For uniform distributions (with different parameters), generate samples of size <math>n = 5, 10, 50, 100, 500</math>.  We shall call these sets of data set 6, set 7, ..., and set 10.
-'''Statisticians''':  Take your friend's generated data, and for each set of data compute the sample mean <math>\bar{X}</math> and the sample variance <math>S^2</math>.
+For the normal distributions, you already know the variances and the standard deviation.  For the uniform distributions, for each set of data, compute the real means, real variances, and  real standard deviations.
 == Confidence interval, known <math>\sigma</math> ==
 == Confidence interval, unknown <math>\sigma</math> ==

@@ แถว 2: / แถว 2: @@
 We will work in pairs.
 '''Generators''':  We shall perform sampling from two random distribution the normal distribution and a uniform distribution over some range <math>[a,b]</math>.
 '''Statisticians''':  Take your friend's generated data, and for each set of data compute the sample mean <math>\bar{X}</math> and the sample variance <math>S^2</math>.

@@ แถว 1: / แถว 1: @@
-== Sample ==
+== Sampling and statistics ==
-<center>
+== Confidence interval, known <math>\sigma</math> ==
-Also recall that the variance of the distribution is
+== Confidence interval, unknown <math>\sigma</math> ==