Probstat/homework 2 - ประวัติรุ่นแก้ไข

Jittat: /* Part 3: Estimations and confidence intervals. */

2014-12-03T06:01:15Z

Part 3: Estimations and confidence intervals.

Jittat: /* Part 3: Estimations and confidence intervals. */

2014-12-01T00:57:25Z

Part 3: Estimations and confidence intervals.

Jittat: /* Part 3: Estimations and confidence intervals. */

2014-12-01T00:56:31Z

Part 3: Estimations and confidence intervals.

Jittat: /* Part 3: Estimations and confidence intervals. */

2014-11-30T22:25:51Z

Part 3: Estimations and confidence intervals.

Jittat: /* Part 3: Estimations and confidence intervals. */

2014-11-30T22:25:23Z

Part 3: Estimations and confidence intervals.

Jittat: /* Part 3: Estimations and confidence intervals. */

2014-11-30T22:25:13Z

Part 3: Estimations and confidence intervals.

Jittat: /* Part 3: Estimations and confidence intervals. */

2014-11-30T22:23:48Z

Part 3: Estimations and confidence intervals.

Jittat: /* Part 2: Distribution of sample means. */

2014-11-30T22:17:33Z

Part 2: Distribution of sample means.

Jittat: /* Part 2: Distribution of sample means. */

2014-11-30T22:17:11Z

Part 2: Distribution of sample means.

Jittat เมื่อ 15:58, 29 พฤศจิกายน 2557

2014-11-29T15:58:33Z

@@ แถว 24: / แถว 24: @@
 == Part 3: Estimations and confidence intervals. ==
-. You take a sample of size 15 from a population with the known variance of 6.  Let <math>\mu</math> be the mean of the population.  What is the probability that the sample mean <math>\bar{X}</math> is such that <math>P\{|\bar{X} - \mu| > 3\}</math>.
+. You take a sample of size 15 from a population with the known variance of 6.  Let <math>\mu</math> be the mean of the population.  What is the probability that the sample mean <math>\bar{X}</math> is such that <math>P\{|\bar{X} - \mu| > 1\}</math>.
-. You take a sample of size 15 from a population with the known variance of 6.  Let <math>\mu</math> be the mean of the population.  What is the probability that the sample mean <math>\bar{X}</math> is such that <math>P\{\bar{X} < \mu - 4\}</math>.
+'''Note:''' this question has be corrected.
 . You take a sample of size 20 from a population with the known variance of 5.   Let <math>\bar{X}</math> be the sample mean.  Find the confidence interval for the confidence level of 90% and 95%.

@@ แถว 47: / แถว 47: @@
 </pre>
-. The following sample is taken from a population whose standard deviation.  Find the sample mean together with the confidence interval with the confidence level of 90%.  Is it possible to say that the population mean is greater than 0 with confidence level 90%?  Why?
+. The following sample is taken from a population whose standard deviation is unknown.  Find the sample mean together with the confidence interval with the confidence level of 90%.  Is it possible to say that the population mean is greater than 0 with confidence level 90%?  Why?
 <pre>

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 00:56, 1 ธันวาคม 2557
แถว 31:		แถว 31:

	4. You take a sample of size 10 from a population with an unknown variance. Let <math>\bar{X}</math> be the sample mean and let <math>S^2</math> be the sample variance. Find the confidence interval for the confidence level of 95% and 99%. (Hint: use t-distribution.)		4. You take a sample of size 10 from a population with an unknown variance. Let <math>\bar{X}</math> be the sample mean and let <math>S^2</math> be the sample variance. Find the confidence interval for the confidence level of 95% and 99%. (Hint: use t-distribution.)
		+
		+	5. The following sample is taken from a population whose standard deviation is 10. Find the sample mean together with the confidence interval with the confidence level of 90%.
		+
		+	<pre>
		+	254.8364581731
		+	232.9768161925
		+	244.2857506108
		+	241.4092424584
		+	238.7415013585
		+	238.8916551149
		+	225.6090880531
		+	243.1193936041
		+	227.8234629926
		+	235.6030158527
		+	</pre>
		+
		+	6. The following sample is taken from a population whose standard deviation. Find the sample mean together with the confidence interval with the confidence level of 90%. Is it possible to say that the population mean is greater than 0 with confidence level 90%? Why?
		+
		+	<pre>
		+	29.6788710493
		+	30.2171658494
		+	10.3209296273
		+	-30.8989271632
		+	-9.6774494881
		+	19.862254862
		+	1.6794611651
		+	-4.5608921106
		+	3.8877580944
		+	-3.1861137644
		+	51.6477880725
		+	17.9539116735
		+	21.3801555032
		+	32.6735671462
		+	6.1932339461
		+	</pre>

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 22:25, 30 พฤศจิกายน 2557
แถว 30:		แถว 30:
	3. You take a sample of size 20 from a population with the known variance of 5. Let <math>\bar{X}</math> be the sample mean. Find the confidence interval for the confidence level of 90% and 95%.		3. You take a sample of size 20 from a population with the known variance of 5. Let <math>\bar{X}</math> be the sample mean. Find the confidence interval for the confidence level of 90% and 95%.

−	4. You take a sample of size 10 from a population with an unknown variance. Let <math>\bar{X}</math> be the sample mean and let <math>S^2</math> be the sample variance. Find the confidence interval for the confidence level of 90% and 95%. (Hint: use t-distribution.)	+	4. You take a sample of size 10 from a population with an unknown variance. Let <math>\bar{X}</math> be the sample mean and let <math>S^2</math> be the sample variance. Find the confidence interval for the confidence level of 95% and 99%. (Hint: use t-distribution.)

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 22:25, 30 พฤศจิกายน 2557
แถว 30:		แถว 30:
	3. You take a sample of size 20 from a population with the known variance of 5. Let <math>\bar{X}</math> be the sample mean. Find the confidence interval for the confidence level of 90% and 95%.		3. You take a sample of size 20 from a population with the known variance of 5. Let <math>\bar{X}</math> be the sample mean. Find the confidence interval for the confidence level of 90% and 95%.

−	3. You take a sample of size 10 from a population with an unknown variance. Let <math>\bar{X}</math> be the sample mean and let <math>S^2</math> be the sample variance. Find the confidence interval for the confidence level of 90% and 95%. (Hint: use t-distribution.)	+	4. You take a sample of size 10 from a population with an unknown variance. Let <math>\bar{X}</math> be the sample mean and let <math>S^2</math> be the sample variance. Find the confidence interval for the confidence level of 90% and 95%. (Hint: use t-distribution.)

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 22:23, 30 พฤศจิกายน 2557
แถว 24:		แถว 24:

	== Part 3: Estimations and confidence intervals. ==		== Part 3: Estimations and confidence intervals. ==
		+	1. You take a sample of size 15 from a population with the know variance of 6. Let <math>\mu</math> be the mean of the population. What is the probability that the sample mean <math>\bar{X}</math> is such that <math>P\{\|\bar{X} - \mu\| > 3\}</math>.
		+
		+	2. You take a sample of size 15 from a population with the know variance of 6. Let <math>\mu</math> be the mean of the population. What is the probability that the sample mean <math>\bar{X}</math> is such that <math>P\{\bar{X} < \mu - 4\}</math>.
		+
		+	3. You take a sample of size 20 from a population with the know variance of 5. Let <math>\bar{X}</math> be the sample mean. Find the confidence interval for the confidence level of 90% and 95%.

@@ แถว 13: / แถว 13: @@
 (a) If we take a sample of size 2, and let <math>\bar{Y}</math> be the sample mean.  Describe the distribution of <math>\bar{Y}</math>.
-(b) If we take a sample of size 3, and let <math>\bar{Y}</math> be the sample mean.  Describe the distribution of <math>\bar{Y}</math>.  (Note: you can write a computer program to help you calculate the distribution.)
+(b) If we take a sample of size 3, and let <math>\bar{Y}</math> be the sample mean.  Describe the distribution of <math>\bar{Y}</math>.  (Note: you can write a computer program to help you calculate the distribution. But if you don't, thinking about 9 cases is not too bad.)
 '''Hint:''' To describe the distribution of normally distributed random variables, you can just specify their means and their variances (or s.d.'s).

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 15:58, 29 พฤศจิกายน 2557
แถว 1:		แถว 1:
−	: ''This is part of [probstat]]''.	+	: ''This is part of [[probstat]]''.

	'''Deadline:''' December 7th, 2014.		'''Deadline:''' December 7th, 2014.