Answer items 4-6: The goal of this exercise is to observe the effect of sampling by treating the 100 SHS students as target population and drawing random samples. The table below shows the height in centimeter of 100 senior high school students at Hope School of Fisheries. Find the population mean height of 100 senior high students. By simple random sampling, take a sample of 10 individuals and record the sample mean. Do this 5 times. That is, you will have a set of 5 sample means (point estimates). Do all sample means from item b vary? How do these sample means compare to the population mean? Repeat (b) but this time take a sample of 20 individuals. How do these sample means compare to the population mean? Repeat (b) but this time take a sample of 35 individuals. How do these sample means compare to the population mean? Describe how the distribution of sample means changes as sample size increases. What is the advantage of a larger sample size? 156 182 154 146 160 156 160 139 162 137 158 145 155 157 150 152 165 149 150 171 162 144 141 156 148 165 157 167 154 169 167 162 166 163 154 129 166 153 164 156 152 160 160 155 162 167 147 160 168 142 135 145 146 150 169 156 186 155 158 156 144 160 148 175 153 157 152 150 158 157 151 165 163 159 173 145 162 157 150 152 144 138 168 158 159 141 161 160 151 163 161 168 164 165 164 139 161 136 173 163

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Answer items 4-6:

The goal of this exercise is to observe the effect of sampling by treating the 100 SHS students as target population and drawing random samples. The table below shows the height in centimeter of 100 senior high school students at Hope School of Fisheries.

1. 1. Find the population mean height of 100 senior high students.
  2. By simple random sampling, take a sample of 10 individuals and record the sample mean. Do this 5 times. That is, you will have a set of 5 sample means (point estimates).
  3. Do all sample means from item b vary? How do these sample means compare to the population mean?
  4. Repeat (b) but this time take a sample of 20 individuals. How do these sample means compare to the population mean?
  5. Repeat (b) but this time take a sample of 35 individuals. How do these sample means compare to the population mean?
  6. Describe how the distribution of sample means changes as sample size increases.
  7. What is the advantage of a larger sample size?

156	182	154	146	160	156	160	139	162	137
158	145	155	157	150	152	165	149	150	171
162	144	141	156	148	165	157	167	154	169
167	162	166	163	154	129	166	153	164	156
152	160	160	155	162	167	147	160	168	142
135	145	146	150	169	156	186	155	158	156
144	160	148	175	153	157	152	150	158	157
151	165	163	159	173	145	162	157	150	152
144	138	168	158	159	141	161	160	151	163
161	168	164	165	164	139	161	136	173	163

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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156	182	154	146	160	156	160	139	162	137
158	145	155	157	150	152	165	149	150	171
162	144	141	156	148	165	157	167	154	169
167	162	166	163	154	129	166	153	164	156
152	160	160	155	162	167	147	160	168	142
135	145	146	150	169	156	186	155	158	156
144	160	148	175	153	157	152	150	158	157
151	165	163	159	173	145	162	157	150	152
144	138	168	158	159	141	161	160	151	163
161	168	164	165	164	139	161	136	173	163

156	182	154	146	160	156	160	139	162	137
158	145	155	157	150	152	165	149	150	171
162	144	141	156	148	165	157	167	154	169
167	162	166	163	154	129	166	153	164	156
152	160	160	155	162	167	147	160	168	142
135	145	146	150	169	156	186	155	158	156
144	160	148	175	153	157	152	150	158	157
151	165	163	159	173	145	162	157	150	152
144	138	168	158	159	141	161	160	151	163
161	168	164	165	164	139	161	136	173	163

156	182	154	146	160	156	160	139	162	137
158	145	155	157	150	152	165	149	150	171
162	144	141	156	148	165	157	167	154	169
167	162	166	163	154	129	166	153	164	156
152	160	160	155	162	167	147	160	168	142
135	145	146	150	169	156	186	155	158	156
144	160	148	175	153	157	152	150	158	157
151	165	163	159	173	145	162	157	150	152
144	138	168	158	159	141	161	160	151	163
161	168	164	165	164	139	161	136	173	163