Question

a) Is a sample correlation coefficient ρ = 0.86 significant at the α = 0.01 level based on a sample size of n = 5 data pairs? What about n = 13 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 = 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 = 13 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.

No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 13 and α = 0.01.

Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 13 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.

No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 13 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.

(b) Is a sample correlation coefficient ρ = 0.41 significant at the α = 0.05 level based on a sample size of n = 19 data pairs? What about n = 26 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 = 26 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 = 19 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 = 26 and α = 0.05.

Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 19 and α = 0.05.

No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 19 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 = 26 and α = 0.05.

Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 26 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 = 19 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.

No, sample size has no bearing on whether or not the correlation coefficient might 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.

Yes, a larger correlation coefficient of 0.70 means that the data will be significant.

Answer 1

a) ρ = 0.86,  α = 0.01

For n = 5

Critical value r = 0.96

As |ρ| = 0.86 < 0.96, we fail to reject the null hypothesis. There is not a correlation.

For n = 13

Critical value r = 0.68

As |ρ| = 0.86 > 0.68, we reject the null hypothesis. There is a correlation.

Answer:

Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 13 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 = 0.41,  α = 0.05

For n = 19

Critical value r = 0.46

As |ρ| = 0.41 < 0.46, we fail to reject the null hypothesis. There is not a correlation.

For n = 26

Critical value r = 0.39

As |ρ| = 0.41 > 0.39, we reject the null hypothesis. There is a correlation.

Answer:

Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 26 and α = 0.05.

No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 19 and α = 0.05.

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