5. The masses measured on a population of 100 animals were grouped in the following table, after being recorded to the nearest gram Mass Frequency 3 89 90-109 110-129 130-149 150-169 170-189 190 7 34 43 10 2 1 You are given that the sample mean of the data is 131.5 and the sample standard deviation is 20.0. Test the hypothesis that the distribution of masses follows a normal distribution at the 5% significance level. Solution: We draw up a table of probabilities. Note that y; is the upper end point of the class. Yi Z₁ -131.5 20 (i) (i) (ži-1 E₁ O₁ 89.5 -2.1 0.0179 0.0179 1.8 3 109.5 -1.1 0.1357 0.1178 11.8 7 129.5 -0.1 0.4602 0.3245 32.4 34 149.5 0.9 0.8159 0.3557 35.6 43 169.5 1.9 0.9713 0.1554 15.5 10 189.5 2.9 0.9981 0.0268 2.7 2 ∞ 1.0000 0.0019 0.2 1 Now to ensure that E; > 5 we merge the first two classes and the last three classes and have the following values of O; and E. O; 10 34 43 13 E 13.6 32.4 35.6 18.4 Null hypothesis Ho: The data are normally distributed.
5. The masses measured on a population of 100 animals were grouped in the following table, after being recorded to the nearest gram Mass Frequency 3 89 90-109 110-129 130-149 150-169 170-189 190 7 34 43 10 2 1 You are given that the sample mean of the data is 131.5 and the sample standard deviation is 20.0. Test the hypothesis that the distribution of masses follows a normal distribution at the 5% significance level. Solution: We draw up a table of probabilities. Note that y; is the upper end point of the class. Yi Z₁ -131.5 20 (i) (i) (ži-1 E₁ O₁ 89.5 -2.1 0.0179 0.0179 1.8 3 109.5 -1.1 0.1357 0.1178 11.8 7 129.5 -0.1 0.4602 0.3245 32.4 34 149.5 0.9 0.8159 0.3557 35.6 43 169.5 1.9 0.9713 0.1554 15.5 10 189.5 2.9 0.9981 0.0268 2.7 2 ∞ 1.0000 0.0019 0.2 1 Now to ensure that E; > 5 we merge the first two classes and the last three classes and have the following values of O; and E. O; 10 34 43 13 E 13.6 32.4 35.6 18.4 Null hypothesis Ho: The data are normally distributed.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 22SGR
Related questions
Question
Please could you explain why 0.5 was added to each upper limpit of the intervals.Thanks
Transcribed Image Text:5. The masses measured on a population of 100 animals were grouped in the
following table, after being recorded to the nearest gram
Mass
Frequency 3
89 90-109 110-129 130-149 150-169 170-189
190
7
34
43
10
2
1
You are given that the sample mean of the data is 131.5 and the sample
standard deviation is 20.0. Test the hypothesis that the distribution of masses
follows a normal distribution at the 5% significance level.
Solution: We draw up a table of probabilities. Note that y; is the upper
end point of the class.
Yi
Z₁
-131.5
20
(i) (i) (ži-1 E₁ O₁
89.5
-2.1
0.0179
0.0179
1.8 3
109.5
-1.1
0.1357
0.1178
11.8 7
129.5
-0.1
0.4602
0.3245
32.4 34
149.5
0.9
0.8159
0.3557
35.6 43
169.5
1.9
0.9713
0.1554
15.5 10
189.5
2.9
0.9981
0.0268
2.7 2
∞
1.0000
0.0019
0.2
1
Now to ensure that E; > 5 we merge the first two classes and the last
three classes and have the following values of O; and E.
O; 10 34 43 13
E 13.6 32.4 35.6 18.4
Null hypothesis Ho: The data are normally distributed.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 3 images
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill