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In: Statistics and Probability
Is a sample correlation coefficient ρ = 0.84 significant at the α = 0.01 level based...
Is a sample correlation coefficient ρ = 0.84 significant at the α = 0.01 level based on a sample size of n = 4 data pairs? What about n = 11 data pairs? (Select all that apply.) No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 11 and α = 0.01. Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 4 and α = 0.01. No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 4 and α = 0.01. Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 4 and α = 0.01. No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 11 and α = 0.01. No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 4 and α = 0.01. Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 11 and α = 0.01. Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 11 and α = 0.01. Incorrect: Your answer is incorrect. (b) Is a sample correlation coefficient ρ = 0.41 significant at the α = 0.05 level based on a sample size of n = 15 data pairs? What about n = 29 data pairs? (Select all that apply.) No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 29 and α = 0.05. Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 29 and α = 0.05. Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 15 and α = 0.05. Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 15 and α = 0.05. Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 29 and α = 0.05. No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 29 and α = 0.05. No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 15 and α = 0.05. No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 15 and α = 0.05. (c) Is it true that in order to be significant, a ρ value must be larger than 0.90? larger than 0.70? larger than 0.50? What does sample size have to do with the significance of ρ? Explain your answer. Yes, a larger correlation coefficient of 0.70 means that the data will be significant. Yes, a larger correlation coefficient of 0.90 means that the data will be significant. Yes, a larger correlation coefficient of 0.50 means that the data will be significant. No, a larger sample size means that a smaller absolute value of the correlation coefficient might be significant. No, sample size has no bearing on whether or not the correlation coefficient might be significant. Correct: Your answer is correct.
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Expert Solution
Is a sample correlation coefficient ρ = 0.84 significant at the α = 0.01 level based on a sample size of n = 4 data pairs? What about n = 11 data pairs? (Select all that apply.)
Critical correlation value at 0.01 level for n=4 is 0.990 and n=11 is 0.735.
Given correlation is not significant at n=4 but significant at n=11.
No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 11 and α = 0.01.
Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 11 and α = 0.01.
(b) Is a sample correlation coefficient ρ = 0.41 significant at the α = 0.05 level based on a sample size of n = 15 data pairs? What about n = 29 data pairs? (Select all that apply.)
Critical correlation value at 0.05 level for n=15 is 0.514 and n=29 is 0.367
Given correlation is not significant at n=15 but significant at n=29
Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 29 and α = 0.05.
No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 15 and α = 0.05.
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