T-test 1 Tcalc is defined as (sqrt(n) × |known value − calculated mean|) / standard deviation.

T-test 1 Tcalc is defined as (sqrt(n) × |known value − calculated mean|) / standard deviation.

• A. (sqrt(n) × |known value − calculated mean|) / standard deviation
• B. (|known value − calculated mean|) / (sqrt(n) × standard deviation)
• C. (sqrt(n) × calculated mean − known value) / standard deviation
• D. (known value − calculated mean) / (n × standard deviation)

Answer: (A)

The main idea is the one-sample t-statistic, which measures how far the sample mean is from a hypothesized population mean in units of the sample standard deviation, scaled by the square root of the sample size. For a two-sided test, you use the absolute value of the difference between the hypothesized mean (known value) and the sample mean (calculated mean). The standard form is t = √n × (x̄ − μ0) / s, and taking the absolute value gives t = √n × |μ0 − x̄| / s. This matches the given expression exactly, where the known value corresponds to μ0, the calculated mean to x̄, and the standard deviation to s. The other forms don’t align with this standard derivation: they either place the √n in the wrong position, remove the square root, misorder the subtraction, or omit the absolute value, which changes the meaning or scale of the statistic. So the expression with √n times the absolute difference between the known value and the calculated mean, divided by the standard deviation, is the correct Tcalc form.

The main idea is the one-sample t-statistic, which measures how far the sample mean is from a hypothesized population mean in units of the sample standard deviation, scaled by the square root of the sample size. For a two-sided test, you use the absolute value of the difference between the hypothesized mean (known value) and the sample mean (calculated mean).

The standard form is t = √n × (x̄ − μ0) / s, and taking the absolute value gives t = √n × |μ0 − x̄| / s. This matches the given expression exactly, where the known value corresponds to μ0, the calculated mean to x̄, and the standard deviation to s.

The other forms don’t align with this standard derivation: they either place the √n in the wrong position, remove the square root, misorder the subtraction, or omit the absolute value, which changes the meaning or scale of the statistic. So the expression with √n times the absolute difference between the known value and the calculated mean, divided by the standard deviation, is the correct Tcalc form.