In a complete randomized design, seven experimental units were used for each of the five levels of the factor. Complete the following ANOVA table
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Source of Variation
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Sum of Squares
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Degrees of Freedom
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Mean Square
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F
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Treatments
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300
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Error
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Total
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460
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1. Determine the critical value for a left-tailed test of a population mean at the α=0.005 level of significance based on a sample size of n = 30.
A) 2.750
B) 2.756
C) -1.699
D) -2.756
E) None of these
2. If beta is computed to be 0.763 , then the power of the test is?
A) 0.737
B) 0.763
C) 0.263
D) 0.237
E) None of these
3. If the probability of getting a sample proportion as exteme or more extreme than the one obtained is small under the assumption the statement in the null hypothesis is true then we reject the null hypothesis.
A) True
B) False
4. Suppose you want to test the claim that u= 3.5 Given a sample size of n = 48 and a level of significance of α=0.01 when should you reject H0?
A) Reject if the standardized test statistic is greater than 2.33 or less than -2.33.
B) Reject if the standardized test statistic is greater than 2.575 or less than -2.575.
C) Reject if the standardized test statistic is greater than 1.96 or less than -1.96.
D) Reject if the standardized test statistic is greater than 1.645 or less than -1.645.
E) None of these
Part I: True - False
1. The mode of a chi-square distribution with 10 degrees of freedom occurs over n = 8.
2. A chi-square test for independence is used to determine whether or not there is an association between the row variable and column variable in a contingency table
3. A p-value is the probability of obtaining a sample statistic as extreme or more extreme than the one observed under the assumption that the statement in the null hypothesis is true.
4. The chi-square distribution is skewed to the left.
5. It is not possible for different levels of significance to lead to different conclusions in a hypothesis test.
6. A zero value of the correlation coefficient "r" says that there is no relationship between the explanatory variable and the response variable.
7. Correlation implies causation.
8. Linear regression equations can be assumed to hold for long periods of time.
10. The null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed and the parameter that is being tested.
11. When referring to entry is a contingency table, what is the exact location of an entry whose location is given by E2,3?
A. Third row, second column
B.Fifth row
C. Fifth column
D. Second row, third column
E. None of these
12. Determine the value of x2 for 17 degrees of freedom and right-tail area of 0.05
a. 27.59 b) 26.30 c) 35.72 d) 25.00 e) None of these
13. Perform the following hypothesis test. The average IQ of Vulcans is quoted as being 212. Thinking this figure is too large, an earthling tested the crew of the first Vulcan ship to land in New Jersey. The average IQ of that 7 member crew was found to be 207 with a sample standard deviation of 10. Perform a statistical test of hypothesis with the null hypothesis of u=212. Use α = 0.05. Show all steps for the P-value method of hypothesis testing. (Be careful not to confuse the P-value approach with the Classical Approach.) Clearly state and and explain their meaning in words.