The sample means and variances of the observed data are needed to find the values in the sum of squares column. The given data are below. Treatment 1 Treatment 2 Treatment 3 Treatment 4 9 5 2 5 6 9 6 1 3 0 1 5 14 4 0 6 1 8 4 5 2 9 0 1 0 5 4 0 9 2 3 0 12 6 3 4 0 9 6 2 2 9 6 1 5 7 7 2 7 14 8 3 3 8 3 3 15 0 0 6 5 5 5 3 4 11 12 7 5 10 9 5 2 10 The sample mean number of pretzels consumed for Treatment 1, rounded to four decimal places, is calculated as follows. x1 = 9 + 6 + 3 + + 11 18 = 6.1111 Find the sample means of the number of pretzels consumed for the remaining treatments, rounding your results to four decimal places. x2 = x3 = x4 = The overall sample mean is the mean of all 74 observations and it will be used in the calculations for the variance. It is calculated below, rounded to four decimal places. = 9 + 6 + + 5 + 9 + + 2 + 6 + + 5 + 1 + + 3 74 = 5.0405 The sample variance of the number of pretzels consumed for Treatment 1 is calculated as follows, with the final result rounded to four decimal places. s12 = x − x 2 n − 1 = (9 − 6.1111)2 + (6 − 6.1111)2 + + (11 − 6.1111)2 17 = 21.9869 Find the remaining sample variances of the number of pretzels consumed for each treatment, rounding the results to four decimal places. s22 = s32 = s42 =
The sample means and variances of the observed data are needed to find the values in the sum of squares column. The given data are below. Treatment 1 Treatment 2 Treatment 3 Treatment 4 9 5 2 5 6 9 6 1 3 0 1 5 14 4 0 6 1 8 4 5 2 9 0 1 0 5 4 0 9 2 3 0 12 6 3 4 0 9 6 2 2 9 6 1 5 7 7 2 7 14 8 3 3 8 3 3 15 0 0 6 5 5 5 3 4 11 12 7 5 10 9 5 2 10 The sample mean number of pretzels consumed for Treatment 1, rounded to four decimal places, is calculated as follows. x1 = 9 + 6 + 3 + + 11 18 = 6.1111 Find the sample means of the number of pretzels consumed for the remaining treatments, rounding your results to four decimal places. x2 = x3 = x4 = The overall sample mean is the mean of all 74 observations and it will be used in the calculations for the variance. It is calculated below, rounded to four decimal places. = 9 + 6 + + 5 + 9 + + 2 + 6 + + 5 + 1 + + 3 74 = 5.0405 The sample variance of the number of pretzels consumed for Treatment 1 is calculated as follows, with the final result rounded to four decimal places. s12 = x − x 2 n − 1 = (9 − 6.1111)2 + (6 − 6.1111)2 + + (11 − 6.1111)2 17 = 21.9869 Find the remaining sample variances of the number of pretzels consumed for each treatment, rounding the results to four decimal places. s22 = s32 = s42 =
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 18PPS
Related questions
Question
The sample means and variances of the observed data are needed to find the values in the sum of squares column. The given data are below.
Treatment 1 | Treatment 2 | Treatment 3 | Treatment 4 |
---|---|---|---|
9 | 5 | 2 | 5 |
6 | 9 | 6 | 1 |
3 | 0 | 1 | 5 |
14 | 4 | 0 | 6 |
1 | 8 | 4 | 5 |
2 | 9 | 0 | 1 |
0 | 5 | 4 | 0 |
9 | 2 | 3 | 0 |
12 | 6 | 3 | 4 |
0 | 9 | 6 | 2 |
2 | 9 | 6 | 1 |
5 | 7 | 7 | 2 |
7 | 14 | 8 | 3 |
3 | 8 | 3 | 3 |
15 | 0 | 0 | |
6 | 5 | 5 | |
5 | 3 | 4 | |
11 | 12 | ||
7 | |||
5 | |||
10 | |||
9 | |||
5 | |||
2 | |||
10 |
The sample mean number of pretzels consumed for Treatment 1, rounded to four decimal places, is calculated as follows.
x1 | = |
|
||
|
||||
= | 6.1111 |
Find the sample means of the number of pretzels consumed for the remaining treatments, rounding your results to four decimal places.
x2 | = | |
|
||
x3 | = | |
|
||
x4 | = |
The overall sample mean
is the mean of all 74 observations and it will be used in the calculations for the variance. It is calculated below, rounded to four decimal places.
= |
|
|||
|
||||
= | 5.0405 |
The sample variance of the number of pretzels consumed for Treatment 1 is calculated as follows, with the final result rounded to four decimal places.
s12 | = |
|
||||||||||
|
||||||||||||
= |
|
|||||||||||
|
||||||||||||
= | 21.9869 |
Find the remaining sample variances of the number of pretzels consumed for each treatment, rounding the results to four decimal places.
s22 | = | |
|
||
s32 | = | |
|
||
s42 | = |
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Follow-up Question
it should be four decimal places..
![X = 2.7142857143
The overall sample mean x is the mean of all 74 observations and it will be used in the calculations for the variance. It is calculated below, rounded to four decimal
places.
9 + 6 + ... + 5 +9 +... + 2 + 6 +... + 5 +1+...
74
= 5.0405
The sample variance of the number of pretzels consumed for Treatment 1 is calculated as follows, with the final result rounded to four decimal places.
s,2 =
n- 1
(9 - 6.1111)? + (6 - 6.1111)2 + ... + (11 - 6.1111)2
17
= 21.9869
Find the remaining sample variances of the number of pretzels consumed for each treatment, rounding the results to four decimal places.
5,2 = 12.59
s3 = 6.24
4.07](https://content.bartleby.com/qna-images/question/52ec1f8a-646f-44a2-abe9-5883d2938c71/2929e74a-0947-4ce5-9a6c-a42984c0d07e/ol16uyb_thumbnail.jpeg)
Transcribed Image Text:X = 2.7142857143
The overall sample mean x is the mean of all 74 observations and it will be used in the calculations for the variance. It is calculated below, rounded to four decimal
places.
9 + 6 + ... + 5 +9 +... + 2 + 6 +... + 5 +1+...
74
= 5.0405
The sample variance of the number of pretzels consumed for Treatment 1 is calculated as follows, with the final result rounded to four decimal places.
s,2 =
n- 1
(9 - 6.1111)? + (6 - 6.1111)2 + ... + (11 - 6.1111)2
17
= 21.9869
Find the remaining sample variances of the number of pretzels consumed for each treatment, rounding the results to four decimal places.
5,2 = 12.59
s3 = 6.24
4.07
Solution
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