1.A researcher wants to investigate whether there is a linear relationship betwe
ID: 3226945 • Letter: 1
Question
1.A researcher wants to investigate whether there is a linear relationship between annual company profit ($) and median annual salary paid by the company ($). The researcher collects data on a random sample of companies and after analyzing the data finds the p-value to be 0.56. Which of the following is an appropriate conclusion based on this p-value?
a.There is not convincing evidence of a linear relationship between annual company profit ($) and median annual salary paid by the company ($).
b.There is no linear relationship between annual company profit ($) and median annual salary paid by the company ($).
cThere is a linear relationship between annual company profit ($) and median annual salary paid by the company ($), and the corresponding value of the correlation coefficient is r = 0.56.
d.There is a 56% chance that there is no linear relationship between annual company profit ($) and median annual salary paid by the company ($).
2The p-value for testing the null hypothesis that there is no linear association between age and maximum legibility distance in the population (versus a two-sided alternative) is less than 0.001. Which of the following are correct interpretations of this value? Select all that apply.
In less than 0.1% of all possible random samples, we would see a sample correlation coefficient of -0.801 or further away from zero, assuming there is no linear relationship between age and maximum legibility distance.
In less than 0.1% of all possible random samples, we would see a sample regression slope of -3.01 or further away from zero, assuming there is no linear relationship between age and maximum legibility distance.
In less than 0.1% of all possible random samples, we would see a sample coefficient of determination of 0.642 or larger, assuming there is no linear relationship between age and maximum legibility distance.
In less than 0.1% of all possible random samples, we would see a sample regression y-intercept of 576.68 or further away from zero, assuming there is no linear relationship between age and maximum legibility distance.
a.There is not convincing evidence of a linear relationship between annual company profit ($) and median annual salary paid by the company ($).
b.There is no linear relationship between annual company profit ($) and median annual salary paid by the company ($).
cThere is a linear relationship between annual company profit ($) and median annual salary paid by the company ($), and the corresponding value of the correlation coefficient is r = 0.56.
d.There is a 56% chance that there is no linear relationship between annual company profit ($) and median annual salary paid by the company ($).
2The p-value for testing the null hypothesis that there is no linear association between age and maximum legibility distance in the population (versus a two-sided alternative) is less than 0.001. Which of the following are correct interpretations of this value? Select all that apply.
In less than 0.1% of all possible random samples, we would see a sample correlation coefficient of -0.801 or further away from zero, assuming there is no linear relationship between age and maximum legibility distance.
In less than 0.1% of all possible random samples, we would see a sample regression slope of -3.01 or further away from zero, assuming there is no linear relationship between age and maximum legibility distance.
In less than 0.1% of all possible random samples, we would see a sample coefficient of determination of 0.642 or larger, assuming there is no linear relationship between age and maximum legibility distance.
In less than 0.1% of all possible random samples, we would see a sample regression y-intercept of 576.68 or further away from zero, assuming there is no linear relationship between age and maximum legibility distance.
Explanation / Answer
1. There is not convincing evidence of a linear relationship between annual company profit ($) and median annual salary paid by the company ($).
Option A is correct.
2. A and B are correct.
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