When using z scores to quantitatively define outliers within a distribution, a score is commonly considered an outlier if it is more than how many standard deviations away from the mean?

A researcher calculates z scores for all participants' reaction times in a cognitive psychology experiment. One participant receives a z score of −2.85. Using the conventional z-score criterion for identifying outliers (i.e., more than three standard deviations from the mean), this participant's reaction time would be classified as an outlier.

In a cognitive psychology experiment measuring reaction times, the sample mean is 400 ms with a standard deviation of 50 ms. Using the standard criterion for outliers (scores with a z score greater than +3.00 or less than -3.00), match each of the following participant reaction times to its correct classification and calculated z score.

In a study investigating adolescent sleep patterns (Mean = 7.5 hours, Standard Deviation = 0.5 hours), a researcher uses z scores to identify potential outliers. Arrange the following sleep durations in order from the least extreme (closest to the mean) to the most extreme (furthest from the mean) to determine which value meets the common criterion for being a statistical outlier.

You are designing a clinical diagnostic scale to identify children with 'extreme social anxiety.' To ensure your tool follows standard statistical conventions for identifying outliers, you want to establish the scoring parameters such that a raw score of $145$ on the scale corresponds exactly to the outlier threshold of $z = +3.00$. If the population mean ($M$) is fixed at $100$, what standard deviation ($SD$) must you ensure the test produces during its standardization phase to meet this design requirement?

According to the common statistical convention in psychological research, a score is classified as an outlier if it has a corresponding $z$ score that is less than $-3.00$ or greater than $+3.00$.

In psychology research, when evaluating the effectiveness of the $z$ score method for outlier detection, researchers must recognize that extreme values can paradoxically mask their own extremity by significantly _____ the standard deviation.

A cognitive psychologist calculates $z$ scores for a dataset of reaction times with a mean of 500 ms and a standard deviation of 50 ms. Match each participant's raw score to its correct classification based on the standard $z$ score outlier threshold.

An analyst is identifying outliers in a dataset. They note that a score is quantitatively classified as an outlier if it is more than _____ standard deviations away from the mean, representing a $z$ score less than $-3.00$ or greater than $+3.00$.

Evaluate the extremity of the following participant $z$ scores and order them from the most extreme low-value outlier to the most extreme high-value outlier based on the standard outlier threshold of $|z| > 3.00$.

Identify the standard quantitative criterion for defining outliers using $z$ scores. In your response, state the relationship between outliers and standard deviations from the mean, and specify the exact threshold $z$ score values commonly used in psychological research.

Explain how the researcher should apply the $z$ score method to identify outliers in the reaction time distribution. Describe the statistical logic of this method, including the specific standard deviation thresholds and corresponding $z$ score values.

An undergraduate student collecting survey data on stress levels finds that one participant has a stress score corresponding to a $z$ score of $+3.40$. Apply the conventional $z$ score outlier threshold to determine whether this participant's stress score is classified as an outlier, and justify your answer.