Question
In: Statistics and Probability
a) Is a sample correlation coefficient ρ = 0.86 significant at the α = 0.01 level...
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.
Solutions
Expert Solution
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.
-----------------
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.
-----------------------
c) No, a larger sample size means that a smaller absolute value of the correlation coefficient might be significant.
orchestra answered 2 years agoRelated Solutions
Is a sample correlation coefficient ρ = 0.84 significant at the α = 0.01 level based...
Is a sample correlation coefficient ρ = 0.83 significant at the α = 0.01 level based...
In a two-tailed test for correlation at α = .05, a sample correlation coefficient r =...
Determine whether the correlation coefficient is statistically significant at the specified level of significance for the...
For Exercises find the critical value from Table L for the rank correlation coefficient, given sample size n and a. Assume that the test is two-tailed. n = 14, α = 0.01
Conduct a test and find if there is a difference at the α=0.01 level of significance....
Conduct the following test at the α=0.01 level of significance by determining (a) the null and...
Conduct the following test at the α=0.01 level of significance by determining (a) the null and...
The coefficient of correlation ρ between these two assets is equal to .009, and the risk free rate is 3.8%.
I want to conduct the following test at the α=0.01 level of significance by determining the...
- Consider the following schema: Suppliers(sid, sname, address) Parts(pid, pname, color) Catalog(sid, pid, cost) write the following...
- Singh Development Co. is deciding whether to proceed with Project X. The cost would be $12...
- CS2123 Data Structures - Fall 2019 Assignment 1: Function Runtimes Table Due 9/11/19 by 11:59pm Completing...
- Question 2. Design a 16-1 MUX using any number of lower MUXs, such as 8-1 or...
- . Write a function that takes, as arguments, two objects, value1 and value2. If
- Wii Brothers, a game manufacturer, has a new idea for an adventure game. It can market...
- Consider the distillation of ethanol (C2H5OH) and the combustion of ethanol . Use a bullet point...