Which scenario is an example of a nondirectional hypothesis? Select an answer: As the outside temperature drops, fewer people go to the beach. A gallon of milk will get colder as the amount of time the milk is in the refrigerator increases. A student’s grade will change as the amount of study time increases. The longer employees work at a company, the more money they will make. How are variance and standard deviation related? Select an answer: Standard deviation is the square root of variance. Variance minus the average equals the standard deviation. One minus the standard deviation equals the variance. Variance is the natural logarithm of standard deviation Which two sets of data have perfect? Select an answer: {1, 2, 3, 4, 5} {5, 4, 3, 2, 1} {1, 1, 1, 1, } {0, 0, 0, 0, 0} {1, 2, 3, 4, 5} {1, 2, 3, 4, 5} {1, 2, 3, 4, 5} {-1, -2, -3, -4, -5}
The Correct Answer and Explanation is:
1. Which scenario is an example of a nondirectional hypothesis?
Answer:
A student’s grade will change as the amount of study time increases.
Explanation:
A nondirectional hypothesis predicts that there will be a change or relationship between two variables but does not specify the direction of that change. It only states that one variable affects another but doesn’t say whether it will increase or decrease.
- “A student’s grade will change as the amount of study time increases” is nondirectional because it does not specify whether grades will improve or worsen with more study time — just that they will change.
By contrast, the other options are directional hypotheses because they specify the direction of the effect:
- “As the outside temperature drops, fewer people go to the beach.” (fewer means a decrease)
- “A gallon of milk will get colder as the amount of time the milk is in the refrigerator increases.” (colder means decrease in temperature)
- “The longer employees work at a company, the more money they will make.” (more money means increase)
2. How are variance and standard deviation related?
Answer:
Standard deviation is the square root of variance.
Explanation:
Variance and standard deviation are both measures of how spread out data points are from the mean (average).
- Variance is the average of the squared differences from the mean. It measures the average squared deviation, which makes it in squared units of the original data (e.g., if data is in meters, variance is in meters squared).
- Standard deviation is the square root of the variance, bringing the units back to the original scale. It tells you, on average, how much each data point differs from the mean.
Because variance is squared, standard deviation is often more interpretable since it’s in the same units as the data.
The other options are incorrect:
- Variance minus average does not equal standard deviation.
- One minus standard deviation does not equal variance.
- Variance is not the natural logarithm of standard deviation.
3. Which two sets of data have perfect correlation?
Answer:
{1, 2, 3, 4, 5} and {1, 2, 3, 4, 5}
Explanation:
Perfect correlation means the two datasets change together in exactly the same way, either positively or negatively, with no deviation. The correlation coefficient (r) in this case is either +1 or -1.
- The sets {1, 2, 3, 4, 5} and {1, 2, 3, 4, 5} are identical, so they have a perfect positive correlation (r = +1).
- The set {1, 2, 3, 4, 5} and {5, 4, 3, 2, 1} have a perfect negative correlation (r = -1), but the question wording seems incomplete (“Which two sets of data have perfect?”). Since it probably means perfect positive correlation, the identical sets are the answer.
- Other pairs either have all identical values (which is constant and does not have correlation) or are inverses with negatives.
