When evaluating a $t$ score of $1.50$, how is the $p$-value determined if 'extreme' is defined as being far from zero in either direction?

In psychological research, evaluating a $t$ score involves determining the probability of obtaining such a result. Based on the example of evaluating a $t$ score of $1.50$ in a two-tailed test, match each component to its correct role or value.

A researcher obtains a $t$ score of $1.50$ and finds that $7\%$ of the distribution falls at or above this value. Sequence the logical steps required to calculate the $p$-value for a two-tailed test, defining 'extreme' as being far from zero in either direction.

When evaluating a $t$ score of $1.50$ based on a sample of $25$, if 'extreme' is defined as being far from zero in either direction, it is a logically sound evaluative decision to define the $p$-value using only the proportion of scores in the distribution that are $1.50$ or above.

You are designing an automated reporting tool for a psychology lab. The tool must 'create' a visual summary for a researcher's $t$ score of $1.50$ based on a sample of $25$. To accurately represent 'extreme' values as being far from zero in either direction (totaling a $p$-value of $.14$), which logic should you program into the tool's visualization module?

When evaluating a $t$ score of $1.50$ and defining 'extreme' as being far from zero in either direction, the $p$-value is determined solely by the proportion of $t$ scores in the distribution that are $1.50$ or above.

A researcher obtains a $t$ score of $1.90$ and finds that the proportion of the distribution at or above this value is $.03$. If the researcher is conducting a two-tailed test (defining 'extreme' as far from zero in either direction), the total $p$-value is _____.

In the example of evaluating a $t$ score of $1.50$ based on a sample of $25$, the two-tailed $p$-value is $.14$. Because the $t$ distribution is symmetric, the proportion of $t$ scores that are $-1.50$ or below must be exactly _____.

A researcher evaluates a $t$ score of $1.50$ from a sample of $n = 25$, defining 'extreme' as being far from zero in either direction. Match each element of this evaluation to the distinct analytical role it plays in determining the $p$-value.

A classmate states: 'I obtained $t = 1.50$ with $n = 25$. The two-tailed $p$-value is $.14$, so I reject the null hypothesis.' You must evaluate whether this interpretation is logically sound, step by step. Place the following evaluative checks in the order they should be performed, from first to last.

Based on the provided example of evaluating a $t$ score of $1.50$ with a sample size of $25$, recall how the probability of obtaining a $t$ score at least this extreme is defined and how the $p$-value is calculated when 'extreme' is defined in either direction.

Explain why evaluating a $t$ score of $1.50$ requires examining both directions of the distribution when 'extreme' is defined as being far from zero, and explain what the resulting $p$-value of $.14$ represents in terms of the null hypothesis distribution.

Suppose a researcher obtains a $t$ score of $1.50$ based on a sample of $25$ but defines 'extreme' as only being far from zero in the positive direction. Using the symmetric nature of the $t$ distribution and the two-tailed $p$-value of $.14$, calculate the new one-tailed $p$-value and explain your calculation in one to three sentences.