Question

Suppose that the sample average is 40.1 while the null hypothesis is that the population mean is 42. If the standard error is 2.5, what is the t-test statistic? (Answer to 4 decimal places)

Answer 1

To find the t-test statistic, subtract the population mean from the sample mean and divide by the standard error. With a sample mean of 40.1, a population mean of 42, and a standard error of 2.5, the t-test statistic is -0.76.

Step-by-step explanation:

To calculate the t-test statistic for this scenario where the sample average is 40.1 and the null hypothesis population mean is 42, with a standard error of 2.5, we use the formula for the t-statistic:

t =
`(\(\bar{x}\) - \(\mu\)) / SE`

Where:

• 
  `\(\bar{x}\)` is the sample mean,
• 
  `\(\mu\)` is the population mean under the null hypothesis, and
• SE is the standard error.

Plugging in our values:

t = (40.1 - 42) / 2.5

t = -1.9 / 2.5

t = -0.76

Therefore, the t-test statistic is -0.76 (rounded to four decimal places).