Question

In this problem, we use your critical values table to explore the significance of r based on different sample sizes. (a) Is a sample correlation coefficient ρ = 0.83 significant at the α = 0.01 level based on a sample size of n = 5 data pairs? What about n = 11 data pairs? (Select all that apply.) 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. 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. 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. 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. No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 5 and α = 0.01. Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 5 and α = 0.01. No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 5 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 = 5 and α = 0.01. Incorrect: Your answer is incorrect. (b) Is a sample correlation coefficient ρ = 0.42 significant at the α = 0.05 level based on a sample size of n = 20 data pairs? What about n = 29 data pairs? (Select all that apply.) No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 20 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 greater than or equal to that for a sample size of n = 20 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. Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 20 and α = 0.05. 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. 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 smaller than that for a sample size of n = 20 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. No, a larger sample size means that a smaller absolute value of the correlation coefficient might be significant. Yes, a larger correlation coefficient of 0.50 means that the data will be significant. Yes, a larger correlation coefficient of 0.90 means that the data will be significant. No, sample size has no bearing on whether or not the correlation coefficient might be significant.

Answer 1

(a) ρ = 0.83, α = 0.01

For n = 5: Critical value, r_c = 0.959

For n = 11: Critical value, r_c = 0.735

Answer: All that apply:

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.

No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 5 and α = 0.01.

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(b) ρ = 0.42, α = 0.05

For n = 20: Critical value, r_c = 0.444

For n = 29: Critical value, r_c = 0.367

Answer: All that apply:

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 = 20 and α = 0.05.

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(c) Answer:

No, a larger sample size means that a smaller absolute value of the correlation coefficient might be significant.