Probstat/week13 practice 1 - ประวัติรุ่นแก้ไข

Jittat: /* Reviews */

2014-11-20T06:01:27Z

Reviews

Jittat: /* Tests concerning the equality means of normal population: known \sigma */

2014-11-20T03:35:30Z

Tests concerning the equality means of normal population: known \sigma

Jittat: /* Tests concerning the equality means of normal population: known \sigma */

2014-11-20T03:34:27Z

Tests concerning the equality means of normal population: known \sigma

Jittat: /* Reviews */

2014-11-20T03:26:51Z

Reviews

Jittat: /* Tests concerning the mean of a population: unknown \sigma */

2014-11-20T01:56:54Z

Tests concerning the mean of a population: unknown \sigma

Jittat เมื่อ 01:56, 20 พฤศจิกายน 2557

2014-11-20T01:56:36Z

Jittat: /* Tests concerning the mean of a population: known \sigma */

2014-11-20T01:55:25Z

Tests concerning the mean of a population: known \sigma

Jittat: /* Tests concerning the mean of a population: unknown \sigma */

2014-11-20T01:55:09Z

Tests concerning the mean of a population: unknown \sigma

Jittat: /* Tests concerning the mean of a population: known \sigma */

2014-11-20T01:53:23Z

Tests concerning the mean of a population: known \sigma

Jittat: /* Tests concerning the mean of a population: known \sigma */

2014-11-20T01:43:21Z

Tests concerning the mean of a population: known \sigma

@@ แถว 8: / แถว 8: @@
 * Find the minimum value <math>T</math> such that <math>P\{|X-50| > T\}\leq 0.01</math>.  You may use computers to compute <math>T</math> exactly.
 * Find the minimum value <math>T</math> such that <math>P\{X > 50 + T\}\leq 0.01</math>.  You may use computers to compute <math>T</math> exactly.
 . What is the variance of <math>X</math> from question 1?

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 03:35, 20 พฤศจิกายน 2557
แถว 37:		แถว 37:
	Suppose that we randomly choose <math>n</math> students from the first group and find the sample mean <math>\bar{X}</math> of their times for 100m runs. Also, we randomly choose <math>m</math> students from the second group and find the sample mean <math>\bar{Y}</math> of times of 100m runs.		Suppose that we randomly choose <math>n</math> students from the first group and find the sample mean <math>\bar{X}</math> of their times for 100m runs. Also, we randomly choose <math>m</math> students from the second group and find the sample mean <math>\bar{Y}</math> of times of 100m runs.

−	We would like to know if the training has any effects on student run times. Describe statistical tests of significant levels <math>\alpha</math> = 0.1, 0.05, and 0.01.	+	We would like to know if the training has any effects on student run times.
		+
		+	1. What is the distribution of <math>\bar{X}</math>?
		+
		+	2. What is the distribution of <math>\bar{Y}</math>?
		+
		+	3. What is the distribution of <math>\bar{X} - \bar{Y}</math>?
		+
		+	4. Describe statistical tests of significant levels <math>\alpha</math> = 0.1, 0.05, and 0.01.

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 03:34, 20 พฤศจิกายน 2557
แถว 33:		แถว 33:

	== Tests concerning the equality means of normal population: known <math>\sigma</math> ==		== Tests concerning the equality means of normal population: known <math>\sigma</math> ==
		+	We have two populations: students who attend special track-and-field training and students who do not attend the training. Let's call the average time for a 100m-run of the first group of students <math>\mu_x</math> and of the second group of students <math>\mu_y</math>. Suppose that we know that the run time are normally distributed with standard deviation <math>\sigma=2</math> seconds.
		+
		+	Suppose that we randomly choose <math>n</math> students from the first group and find the sample mean <math>\bar{X}</math> of their times for 100m runs. Also, we randomly choose <math>m</math> students from the second group and find the sample mean <math>\bar{Y}</math> of times of 100m runs.
		+
		+	We would like to know if the training has any effects on student run times. Describe statistical tests of significant levels <math>\alpha</math> = 0.1, 0.05, and 0.01.

@@ แถว 4: / แถว 4: @@
 . We toss a fair coin 100 times.  Let random variable <math>X</math> be the number of heads.
-* Find the minimum value <math>T</math> such that <math>P\{|X-50| > T\}\leq 0.5</math>.  You may use computers to compute <math>T</math> exactly.
+* Find the minimum value <math>T</math> such that <math>P\{|X-50| > T\}\leq 0.05</math>.  You may use computers to compute <math>T</math> exactly.
-* Find the minimum value <math>T</math> such that <math>P\{X > 50 + T\}\leq 0.5</math>.  You may use computers to compute <math>T</math> exactly.
+* Find the minimum value <math>T</math> such that <math>P\{X > 50 + T\}\leq 0.05</math>.  You may use computers to compute <math>T</math> exactly.
 * Find the minimum value <math>T</math> such that <math>P\{|X-50| > T\}\leq 0.01</math>.  You may use computers to compute <math>T</math> exactly.
 * Find the minimum value <math>T</math> such that <math>P\{X > 50 + T\}\leq 0.01</math>.  You may use computers to compute <math>T</math> exactly.
@@ แถว 13: / แถว 13: @@
 . Let's approximate <math>X</math> from question 1 with the normal distribution.
-* Find the minimum value <math>T</math> such that <math>P\{|X-50| > T\}\leq 0.5</math>.  Use the standard normal distribution table to answer this.  Compare with the answer from question 1.
+* Find the minimum value <math>T</math> such that <math>P\{|X-50| > T\}\leq 0.05</math>.  Use the standard normal distribution table to answer this.  Compare with the answer from question 1.
-* Find the minimum value <math>T</math> such that <math>P\{X > 50 + T\}\leq 0.5</math>.  Use the standard normal distribution table to answer this.  Compare with the answer from question 1.
+* Find the minimum value <math>T</math> such that <math>P\{X > 50 + T\}\leq 0.05</math>.  Use the standard normal distribution table to answer this.  Compare with the answer from question 1.
 * Find the minimum value <math>T</math> such that <math>P\{|X-50| > T\}\leq 0.01</math>.  Use the standard normal distribution table to answer this.  Compare with the answer from question 1.
 * Find the minimum value <math>T</math> such that <math>P\{X > 50 + T\}\leq 0.01</math>.  Use the standard normal distribution table to answer this.  Compare with the answer from question 1.

@@ แถว 29: / แถว 29: @@
 '''Hint:''' your tests should specify the conditions to reject <math>H_0</math> and should depend on <math>\bar{X}</math> and <math>S</math>.
 . Consider the tests you design from question 1.  What is the probability that the tests accept <math>H_0</math> when the actual speed is 9.5Mbps?
 == Tests concerning the equality means of normal population: known <math>\sigma</math> ==

@@ แถว 20: / แถว 20: @@
 == Tests concerning the mean of a population: known <math>\sigma</math> ==
 . An ISP claims to provide an Internet connection with the speed of 10Mbps.  You know that the speed is normally distributed with s.d. <math>\sigma = 1.5</math>.  You plan to obtain a sample of size 10 of the Internet connection speed, and compute the sample mean <math>\bar{X}</math>.  Design 3 statistical tests with levels of significances <math>\alpha</math> = 0.1, 0.05, and 0.01 to show if we should believe the claim from the ISP.  Define explicitly what your null hypothesis <math>H_0</math> is.
 . Consider the tests you design from question 1.  What is the probability that the tests accept <math>H_0</math> when the actual speed is 9.5Mbps?
@@ แถว 26: / แถว 28: @@
 . An ISP claims to provide an Internet connection with the speed of 10Mbps.  You know that the speed is normally distributed but you do not know <math>\sigma</math>.  You plan to obtain a sample of size 10 of the Internet connection speed, and compute the sample mean <math>\bar{X}</math> and the sample standard deviation <math>S</math>.  Design 3 statistical tests with levels of significances <math>\alpha</math> = 0.1, 0.05, and 0.01 to show if we should believe the claim from the ISP.  Define explicitly what your null hypothesis <math>H_0</math> is.
 . Consider the tests you design from question 1.  What is the probability that the tests accept <math>H_0</math> when the actual speed is 9.5Mbps?
 == Tests concerning the equality means of normal population: known <math>\sigma</math> ==

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 01:55, 20 พฤศจิกายน 2557
แถว 24:		แถว 24:

	== Tests concerning the mean of a population: unknown <math>\sigma</math> ==		== Tests concerning the mean of a population: unknown <math>\sigma</math> ==
		+	1. An ISP claims to provide an Internet connection with the speed of 10Mbps. You know that the speed is normally distributed but you do not know <math>\sigma</math>. You plan to obtain a sample of size 10 of the Internet connection speed, and compute the sample mean <math>\bar{X}</math> and the sample standard deviation <math>S</math>. Design 3 statistical tests with levels of significances <math>\alpha</math> = 0.1, 0.05, and 0.01 to show if we should believe the claim from the ISP. Define explicitly what your null hypothesis <math>H_0</math> is.
		+
		+	2. Consider the tests you design from question 1. What is the probability that the tests accept <math>H_0</math> when the actual speed is 9.5Mbps?

	== Tests concerning the equality means of normal population: known <math>\sigma</math> ==		== Tests concerning the equality means of normal population: known <math>\sigma</math> ==

@@ แถว 19: / แถว 19: @@
 == Tests concerning the mean of a population: known <math>\sigma</math> ==
-. An ISP claims to provide an Internet connection with the speed of 10Mbps.  You know that the speed is normally distributed with s.d. <math>\sigma = 1.5</math>.  You plan to obtain a sample of size 10 of the Internet connection speed.  Design 3 statistical tests with levels of significances <math>\alpha = 0.1, 0.05, 0.01</math> to show if we should believe the claim from the ISP.  Define explicitly what your null hypothesis <math>H_0</math> is.
+. An ISP claims to provide an Internet connection with the speed of 10Mbps.  You know that the speed is normally distributed with s.d. <math>\sigma = 1.5</math>.  You plan to obtain a sample of size 10 of the Internet connection speed.  Design 3 statistical tests with levels of significances <math>\alpha</math> = 0.1, 0.05, and 0.01 to show if we should believe the claim from the ISP.  Define explicitly what your null hypothesis <math>H_0</math> is.
 == Tests concerning the mean of a population: unknown <math>\sigma</math> ==
 == Tests concerning the equality means of normal population: known <math>\sigma</math> ==