How do you calculate a t value?

How do you calculate a t value?

• A. (sample mean - mean)/sample SD
• B. (sample mean - mean)/standard error
• C. (observed proportion - expected proportion)/standard error
• D. (variance) / n

Answer: (A)

When you compute a t value, you’re asking how far the observed sample mean is from the hypothesized population mean, but in units that reflect how precisely you’ve estimated that mean. The formula you use is t = (Xbar − μ0) / (s / sqrt(n)). Here Xbar is the sample mean, μ0 is the value under the null hypothesis, s is the sample standard deviation, and n is the sample size. The denominator is the standard error of the mean (s divided by the square root of n), which captures sampling variability and shrinks as you collect more data. Degrees of freedom for a one-sample t-test are n − 1. In the provided options, the correct approach uses the standard error (the division by sqrt(n) is essential); using only the sample standard deviation in the denominator does not yield the t statistic.

When you compute a t value, you’re asking how far the observed sample mean is from the hypothesized population mean, but in units that reflect how precisely you’ve estimated that mean. The formula you use is t = (Xbar − μ0) / (s / sqrt(n)). Here Xbar is the sample mean, μ0 is the value under the null hypothesis, s is the sample standard deviation, and n is the sample size. The denominator is the standard error of the mean (s divided by the square root of n), which captures sampling variability and shrinks as you collect more data. Degrees of freedom for a one-sample t-test are n − 1. In the provided options, the correct approach uses the standard error (the division by sqrt(n) is essential); using only the sample standard deviation in the denominator does not yield the t statistic.