Final answer:
A Z-score conversion chart is primarily used to calculate the area under a curve, to determine the critical p-value in hypothesis testing, and to convert raw scores to standardized scores. It is not used to measure angles of elevation.
Step-by-step explanation:
A Z-score conversion chart can be utilized in several different scenarios within statistics. Primarily, you can employ a Z-score table:
- Option 1: To calculate the area under a curve. You can use the Z-score to find the probability of a score occurring within a normal distribution, which is depicted as the area under the curve.
- Option 2: To determine the critical p-value. This is related to hypothesis testing where the Z-score assists in deciding whether to reject the null hypothesis.
- Option 3: To convert raw scores to standardized scores. The process involves using the Z-score to standardize scores from different data sets to a common scale.
- Option 4: It is not used to measure the angle of elevation, which is unrelated to Z-scores and involves trigonometry instead.
The Z-score itself tells you how many standard deviations a value is from the mean of its distribution. Positive Z-scores indicate values above the mean, while negative ones represent values below the mean. If a Z-score is 0, it means the value is equivalent to the mean.
These Z-scores are pivotal for comparing values from different data sets with various means and standard deviations. Utilizing the Z-score, you can determine the proportion of data within certain intervals, such as the percentage of values lying within one, two, or three standard deviations from the mean, often referred to as the empirical rule or 68-95-99.7 rule.