Question

1. Which of the following statements is true?

1. The correlation coefficient (r) equals the proportion of times two variables lie on a straight line.
2. The correlation coefficient (r) will be +1 only if all the data lie on a perfectly horizontal straight line.
3. The correlation coefficient (r) measures the fraction of outliers that appear in a scatterplot.
4. The correlation coefficient (r) is a unit-less number and must always lie between –1 and +1, inclusive

2. An entomologist writes an article in a scientific journal which claims that fewer than 10 in ten thousand male fireflies are able to produce light due to genetic mutation. Identify the Type I error for the test.   

1. The error of failing to reject that the true proportion is at least 10 in ten thousand when it is actually less than 10 in ten thousand.
2. The error of rejecting that the true proportion is less than 10 in ten thousand when it is actually less than 10 in ten thousand.
3. The error of rejecting that the true proportion is at least 10 in ten thousand when it is actually at least 10 in ten thousand.
4. The error of failing to reject that the true proportion is less than 10 in ten thousand when it is actually is at least 10 in ten thousand.

3. What does the correlation coefficient (r) measure?   

1. Whether there is a relationship between two variables
2. Whether or not a scatter diagram shows an interesting pattern
3. Whether a cause and effect relation exists between two variables
4. The strength of any straight line relation between two variables

4. Which statement is true for any density curve?

1. It is symmetric.
2. The total area under the curve is one.
3. It must either steadily rise or steadily fall, since it cannot do both.
4. It has all of these properties.

Answer 1

1. The correlation coefficient (r) is a unit-less number and must always lie between –1 and +1, inclusive..hence d is true...
2. The error of rejecting that the true proportion is at least 10 in ten thousand when it is actually at least 10 in ten thousand...as this is the probability of rejecting null when it is true...hence C is the ans
3. The correlation coefficient measures whether there is relationship between two variables(a)
4. For density curve the total area under the curve is one(b)