Question

In: Statistics and Probability

Use the following contingency table to complete​. A B C Total 1 10 25 55 90...

Use the following contingency table to complete​.

A B C Total
1 10 25 55 90
2 40 50 60 150
Total 50 75 115 240

a. Compute the expected frequencies for each cell.

b. Set up the null and alternative hypotheses to test.

c. Compute X2STAT Is it significant at α=0.01​?

d. Compute P-Value

e.Is X2STAT significant at α=0.01​?

Solutions

Expert Solution

(a) The second table contains the expected values.

Chi-Square Independence test - Results
(b) Null and Alternative Hypotheses
The following null and alternative hypotheses need to be tested:
H0​: The two variables are independent
Ha​: The two variables are dependent

This corresponds to a Chi-Square test of independence.

Degrees of Freedom
The number of degrees of freedom is df = (2 - 1) * (3 - 1) = 2

Critical value and Rejection Region
Based on the information provided, the significance level is α=0.01, the number of degrees of freedom is df = (2 - 1) * (3 - 1) = 2, so the critical value is 9.2103.
Then the rejection region for this test becomes R={χ2:χ2>9.2103}.

(c)Test Statistics
The Chi-Squared statistic is computed as follows:

(d)P-value
The corresponding p-value for the test is p=Pr(χ2​>12.3208)=0.0021

(e)The decision about the null hypothesis
Since it is observed that χ2=12.3208>χ2_c​rit=9.2103, it is then concluded that the null hypothesis is rejected.

Conclusion
It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the two variables are dependent, at the 0.01 significance level.

Conditions:
a. The sampling method is simple random sampling.
b. The data in the cells should be counts/frequencies
c. The levels (or categories) of the variables are mutually exclusive.

orchestra answered 2 years ago
Next > < Previous

Related Solutions

Use the following contingency table to complete​ (a) and​ (b) below. A B C Total 1...
Use the following contingency table to complete​ (a) and​ (b) below. A B C Total 1 15 35 40 90 2 30 35 45 110 Total 45 70 85 200 (a). Compute the expected frequencies for each cell. (b) Compute χ2STAT. Is it significant at α=0.01​?
Use the following contingency table to complete​ (a) and​ (b) below. A B C Total 1...
Use the following contingency table to complete​ (a) and​ (b) below. A B C Total 1 15 30 45 90 2 45 50 55 150 Total 60 80 100 240 a. Compute the expected frequencies for each cell. A B C 1 2 ​(Type integers or​ decimals.) b. Compute χ2STAT. is it significant at α=0.005​? Set up the null and alternative hypotheses to test. Choose the correct answer below. H0​: πA= πB= πC H1​:Not all πj are equal​ (where j=​A,...
use the following contingency table a b c total 1 15 30 45 90 2 40...
use the following contingency table a b c total 1 15 30 45 90 2 40 45 50 135 total 55 75 95 225 a. compute the expected frequency for each cell b. compute x^2stat. is it significant at a=0.01
1. Use Table A to Complete Table B. Table A On Taxable Income The Tax Rate...
1. Use Table A to Complete Table B. Table A On Taxable Income The Tax Rate Is Up to $27,050 20.0% From $27,051 to $65,550 27.5% From $65,551 to $136,750 30.5% From $136,751 to $297,350 35.5% Over $297,350 39.1% Table B Taxpayer Income Tax Amount Average Tax Rate Mariginal Tax Rate Giannis $52,700 Sue $132,500 Damian $237,000 Breanna $315,250 2. Bryce loves baseball. During the entire baseball season (every day from mid-March until the end of October), Byrce will watch...
1. Show that the following wff is a contingency. (A → B) ∧ (B → ¬A)...
1. Show that the following wff is a contingency. (A → B) ∧ (B → ¬A) → A. 2. Show that the following wff is a tautology. (A → (B → C)) → ((A → B) → (A → C)). 3. Determine if the following wff is a tautology, contradiction, or a contingency. (A ∨ B) → (C ∨ A) ∧ (¬C ∨ B). 4. Write down the full DNF or full CNF of the following wff (P → ¬Q)...
Complete the following table. (All solutions are at 25 ∘C.) [H3O+] [OH−] pH Acidic or Basic...
Complete the following table. (All solutions are at 25 ∘C.) [H3O+] [OH−] pH Acidic or Basic 3.5×10−3 _____ _____ _____ _____ 3.8×10−7 _____ _____ 1.8×10−9 _____ _____ _____ _____ _____ 7.15 _____ Part A Complete the first column. Express your answers using two significant figures. Enter your answers numerically separated by commas. [H3O+]2, [H3O+]4 = nothing   M   SubmitRequest Answer Part B Complete the second column. Express your answers using two significant figures. Enter your answers numerically separated by commas. [OH−]1,...
The following table shows the total costs for each of four firms (A, B, C, and...
The following table shows the total costs for each of four firms (A, B, C, and D) to eliminate units of pollution from their production processes. For example, for Firm A to eliminate one unit of pollution, it would cost $46, and for Firm A to eliminate two units of pollution, it would cost a total of $103. Firm Unit to be eliminated A B C D One unit 46 45 42 49 Two units 103 100 98 108 Three...
A, B and C, all individuals, own, respectively, 25%, 20% and 55% of X Corp. Their
A, B and C, all individuals, own, respectively, 25%, 20% and 55% of X Corp. Their bases in their stock interests are $2,500, $200, and $4,000, respectively. X has the following items of tax significance for the current year: gross profits, $20,000; depreciation, $8,000; interest expense, $2,000; charitable contributions, $500; long-term capital gain, $5,000. (a) How do these results effect the individual tax returns of A, B and C?(b) Suppose that A had bought her interest from another individual D...
31. Use Table A to complete Table B. TABLE A On Taxable Income The Tax Rate...
31. Use Table A to complete Table B. TABLE A On Taxable Income The Tax Rate Is Up to $27,050 20.0% From $27,051 to $65,550 27.5% From $65,551 to $136,750 30.5% From $136,751 to $297,350 35.5% Over $297,350 39.1% TABLE B Taxpayer Income Tax Amount Average Tax Rate Giannis $52,700 Sue $132,500 Damian $237,000 Breanna $315,250 Marginal Tax Rate
You will create a datafile with the following information: 70 80 90 55 25 62 45...
You will create a datafile with the following information: 70 80 90 55 25 62 45 34 76 105You will then write the program to read in the values from the datafile and as you read in each number, you will then evaluate it through an if statement for the weather of the day. For example, when you read in the value 70 from the datafile, you should print to the screen that the temperature is 70° and it is...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT