Z-Score
Definition
A z-score is a measure of how many standard deviations an individual data point is away from the mean of a distribution. It helps to determine the relative position of a data point within a dataset.
Analogy
Think of a z-score as a GPS for data points. It tells you exactly where each data point is located in relation to the mean, just like GPS coordinates tell you where you are in relation to your destination.
Related terms
Standard Deviation: A measure of how spread out the values in a dataset are around the mean.
Normal Distribution: A symmetric bell-shaped curve that represents many natural phenomena and is commonly used in statistics.
Outlier: An extreme value that significantly differs from other values in a dataset.
"Z-Score" appears in:
Subjects (1)
Study guides (5)
AP Statistics - 1.10 The Normal Distribution
AP Statistics - 6.4 Setting Up a Test for a Population Proportion
AP Statistics - 6.6 Concluding a Test for a Population Proportion
AP Statistics - 6.8 Confidence Intervals for the Difference of Two Proportions
AP Statistics - 6.11 Carrying Out a Test for the Difference of Two Population Proportions
Additional resources (1)
Practice Questions (20+)
How can a z-score be used to conclude a hypothesis test?
In a hypothesis test, a z-score of -1.5 is obtained. What is the appropriate conclusion?
What does a small z-score indicate in a hypothesis test?
In a hypothesis test, the calculated z-score is 2.1. What is the appropriate conclusion?
In a hypothesis test, a z-score of 3.2 is obtained. What is the appropriate conclusion?
What does a large z-score indicate in a hypothesis test?
Which formula is used to calculate the z-score in a test for the difference in two population proportions?
What does it mean if the z-score in a test for the difference in two population proportions is higher than 2 or 3?
In the given example comparing the shooting performance of Michael Jordan and Lebron James, if the z-score is 5.5, what conclusion can be drawn?
What is the purpose of calculating a z-score in a test for the difference in two population proportions?
A researcher is using a z-score to perform a significance test for the difference in two population proportions. The calculated z-score is -1.8. What can the researcher conclude?
To calculate the z-score in a one-proportion z-test, we compare the observed value, which is the sample proportion, to:
A study investigates the effectiveness of a new drug in treating a particular condition. The researchers claim that the drug has a success rate of 80% in the population. To test this claim, a random sample of 500 patients who have taken the drug is selected. The sample proportion of successful outcomes is found to be 0.75. What is the z-score for this one-proportion z-test?
If you conduct a two-sided one-proportion z-test and calculate the z-score of the sample proportion to be -1.235, what is the p-value?
A presidential candidate claims that 56% of voters support him. To test this claim, a poll randomly samples 500 registered voters and finds that 275 of the voters support the candidate. If a one-proportion z-test is to be conducted, what is its z-score?
What does a z-score indicate in relation to the mean in a normal distribution?
What does a z-score of -3 represent in a normal distribution?
What does a z-score of 4 represent in a normal distribution?
What does a z-score of 0 represent in a normal distribution?
Which equation can you use to calculate the z-score?
Resources
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