Concept explainers
The following four
HINTS:
• Calculate the expected frequencies for each cell with Formula 10.2. Double check to make sure you are using the correct row and column marginals for each cell.
• It may he helpful to record the expected frequencies in table format—see Tables 10.4 and 10.8.
• Use a computational table to organize the calculation for Formula 10.1—see Tables 10.5 and 10.9.
• Follow the step-by-step instructions.
• Double-check to make sure you are using the correct values for each cell.
a. |
|
|
|
c. |
|
|
|
|
|
|
|
|
|
||
b. |
|
|
|
d. |
|
|
|
|
|
|
|
|
|
(a)
To find:
The chi square value for the given information.
Answer to Problem 10.1P
Solution:
The chi square value is 1.12.
Explanation of Solution
Given:
The given table of information is,
a. | |||
Description:
The confidence interval is an interval estimate from the statistics of the observed data that might contain the true value of the unknown population parameter.
Formula used:
For a chi square, the expected frequency
Where N is the total of frequencies.
The chi square statistic is given by,
Where
And
Calculation:
From the given information,
The row marginal is 45, the column marginal is 45 and N is 90.
The observed frequency is given as,
Substitute 45 for row marginal, 45 for column marginal and 90 for N in the above formula.
Consider the following table,
20 | 22.5 | 0.28 | |||
25 | 22.5 | 0.28 | |||
25 | 22.5 | 0.28 | |||
20 | 22.5 | 0.28 | |||
Total | 90 | 90 | 0 |
The value
Substitute 20 for
Squaring the above obtained result,
Divide the above obtained result by
Proceed in a similar manner to obtain rest of the values of
The chi square value is given as,
Thus, the chi square value is 1.12.
Conclusion:
The chi square value is 1.12.
(b)
To find:
The chi square value for the given information.
Answer to Problem 10.1P
Solution:
The chi square value is 0.0.
Explanation of Solution
Given:
The given table of information is,
b. | 10 | 15 | 25 |
20 | 30 | 50 | |
30 | 45 | 75 |
Description:
The confidence interval is an interval estimate from the statistics of the observed data that might contain the true value of the unknown population parameter.
Formula used:
For a chi square, the expected frequency
Where N is the total of frequencies.
The chi square statistic is given by,
Where
And
Calculation:
From the given information,
The observed frequency is given as,
Substitute 25 for row marginal, 30 for column marginal and 75 for N in equation
Substitute 25 for row marginal, 45 for column marginal and 75 for N in equation
Substitute 50 for row marginal, 30 for column marginal and 75 for N in equation
Substitute 50 for row marginal, 45 for column marginal and 75 for N in equation
Consider the following table,
10 | 10 | 0 | 0 | 0 | |
15 | 15 | 0 | 0 | 0 | |
20 | 20 | 0 | 0 | 0 | |
30 | 30 | 0 | 0 | 0 | |
Total | 75 | 75 | 0 | 0 |
The value
Substitute 10 for
Squaring the above obtained result,
Divide the above obtained result by
Proceed in a similar manner to obtain rest of the values of
The chi square value is given as,
Thus, the chi square value is 0.0.
Conclusion:
The chi square value is 0.0.
(c)
To find:
The chi square value for the given information.
Answer to Problem 10.1P
Solution:
The chi square value is 1.51.
Explanation of Solution
Given:
The given table of information is,
c. | 25 | 15 | 40 |
30 | 30 | 60 | |
55 | 45 | 100 |
Description:
The confidence interval is an interval estimate from the statistics of the observed data that might contain the true value of the unknown population parameter.
Formula used:
For a chi square, the expected frequency
Where N is the total of frequencies.
The chi square statistic is given by,
Where
And
Calculation:
From the given information,
The observed frequency is given as,
Substitute 40 for row marginal, 55 for column marginal and 100 for N in equation
Substitute 40 for row marginal, 45 for column marginal and 100 for N in equation
Substitute 60 for row marginal, 55 for column marginal and 100 for N in equation
Substitute 60 for row marginal, 45 for column marginal and 100 for N in equation
Consider the following table,
25 | 22 | 3 | 9 | 0.41 | |
15 | 18 | 9 | 0.50 | ||
30 | 33 | 9 | 0.27 | ||
30 | 27 | 3 | 9 | 0.33 | |
Total | 100 | 100 | 0 |
The value
Substitute 25 for
Squaring the above obtained result,
Divide the above obtained result by
Proceed in a similar manner to obtain rest of the values of
The chi square value is given as,
Thus, the chi square value is 1.51.
Conclusion:
The chi square value is 1.51.
(d)
To find:
The chi square value for the given information.
Answer to Problem 10.1P
Solution:
The chi square value is 1.43.
Explanation of Solution
Given:
The given table of information is,
d. | 20 | 45 | 65 |
15 | 20 | 35 | |
35 | 65 | 100 |
Description:
The confidence interval is an interval estimate from the statistics of the observed data that might contain the true value of the unknown population parameter.
Formula used:
For a chi square, the expected frequency
Where N is the total of frequencies.
The chi square statistic is given by,
Where
And
Calculation:
From the given information,
The observed frequency is given as,
Substitute 65 for row marginal, 35 for column marginal and 100 for N in equation
Substitute 65 for row marginal, 65 for column marginal and 100 for N in equation
Substitute 35 for row marginal, 35 for column marginal and 100 for N in equation
Substitute 35 for row marginal, 65 for column marginal and 100 for N in equation
Consider the following table,
20 | 22.75 | -2.75 | 7.5625 | 0.332417582 | |
45 | 42.25 | 2.75 | 7.5625 | 0.178994083 | |
15 | 12.25 | 2.75 | 7.5625 | 0.617346939 | |
20 | 22.75 | 7.5625 | 0.332417582 | ||
Total | 100 | 100 | 0 |
The value
Substitute 20 for
Squaring the above obtained result,
Divide the above obtained result by
Proceed in a similar manner to obtain rest of the values of
The chi square value is given as,
Thus, the chi square value is 1.46.
Conclusion:
The chi square value is 1.46.
Want to see more full solutions like this?
Chapter 10 Solutions
Essentials of Statistics: A Tool for Social Research - With SPSS DVD
- Select the measurement scale in the right column that best matches the description in the left column. Note that each scale (nominal scale, ordinal scale, interval scale, and ratio scale) will be used exactly once. The values of data measured on this scale can be rank ordered. In addition, the differences between two adjacent ranks are equal. The values of data measured on this scale can be a number or a name, but they can be rank ordered. The values of data measured on this scale can be rank ordered and have meaningful differences between scale points. For this scale, there is also an absolute zero point. Data on this scale are measured by determining the category to which they belong.arrow_forwardUsing the given data, find the following. 468 324 175 439 407 355 261 436 435 135 220 Send data to Excel Part 1 of 2 Identify the five-number summary. Round your answers to one decimal place as needed. Low =| 135 , Q, = | 241 MD = 355 Q2 = 436 High =468 Correct Answer: Low = 135, Q1=220, MD = 355, Q3 = 436, High = 468 Part: 1/2 Part 2 of 2 Find the interquartile range. Round your answer to one decimal place as needed. IQR =arrow_forwardPLEASE ANSWER A, B AND Carrow_forward
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning