Exhibit 9-1.A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50.A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60.The population standard deviation is assumed to equal 0.40. Refer to Exhibit 9-1.The value of the test statistic is ____________.

Question

Quizplus · Accepted Answer

The test statistic for a one-sample t-test is calculated as:

t = (sample mean - hypothesized population mean) / (sample standard error)

Here, the hypothesized population mean is 3.50, the sample mean is 3.60 and the sample size is 36. The sample standard error is equal to the population standard deviation divided by the square root of the sample size:

SE = σ/√n = 0.40/√36 = 0.0667

Plugging these values into the formula for t, we get:

t = (3.60 - 3.50) / 0.0667 = 1.50/0.0667 = 22.5

Therefore, the value of the test statistic is 22.5, which corresponds to choice C.