A university conducted a study on 446 business graduates who had all completed t
ID: 3049995 • Letter: A
Question
A university conducted a study on 446 business graduates who had all completed the same business course. The study used correlation coefficients to investigate the relationship between many different business skills. Two of the many variables measured were self-knowledge skill level (x) and goalsetting ability (y). The correlation coefficient was .r=0.78 Complete parts a through c below.
a. Give a practical interpretation of the value of r. Choose the correct answer below.
A. Since the value of r is fairly large, there is a moderately strong positive linear relationship between self-knowledge skill level and goalsetting ability.
B. Since the value of r is fairly large, there is a weak positive linear relationship between self-knowledge skill level and goalsetting ability.
C. Since the value of r is less than 0.90, there is a weak positive linear relationship between self-knowledge skill level and goalsetting ability.
b. The p-value for a test of no correlation between the two variables was reported as p font size decreased by pvalue=0.001. Interpret this result. Choose the correct answer below.
A. Since the p-value is so small, there is sufficient evidence to reject the null hypothesis. There is evidence to indicate a linear relationship between self-knowledge skill level and goalsetting ability for any significance level of >0.001.
B. Since the p-value is so small, there is sufficient evidence to reject the null hypothesis. There is evidence to indicate a significant negative linear relationship between self-knowledge level skill and goalsetting ability for any significance level of >0.001.
C. Since the p-value is so small, do not reject the null hypothesis.
c. Find the coefficient of determination, r2, and interpret the result.
r2=______ (Round to four decimal places as needed.)
Interpret the result.
A. The linear model explains (1minusr2) times •100% of the total sample variability around the sample mean goalsetting ability.
B. The linear model explains r2 times •100% of the total sample variability around the sample mean goalsetting ability.
C. The linear model explains (1minusr2) times •100% of the total sample variability around the sample mean self-knowledge skill level.
D. The linear model explains r2 times •100% of the total sample variability around the sample mean self-knowledge skill level.
Explanation / Answer
a) Since the value of r is fairly large, there is a moderately strong positive linear relationship between self-knowledge skill level and goalsetting ability. Option A is correct.
b) Since the p-value is so small, there is sufficient evidence to reject the null hypothesis. There is evidence to indicate a linear relationship between self-knowledge skill level and goalsetting ability for any significance level of >0.001. Option A is correct.
c) r2 = 0.872 = 0.7569
The linear model explains r2 times •100% of the total sample variability around the sample mean goalsetting ability. Option B is correct.
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