Question

A researcher is performing a hypothesis test. The null hypothesis is that μ=10 and the alternative hypothesis is that μ<10. A sample of 18 individuals was collected and the t-based test statistic calculated from the data was -2.105. What is the approximate p-value for this hypothesis test?

Answer 1

To find the p-value for this hypothesis test, we need to find the area under the t-distribution curve to the left of the test statistic, t = -2.105. Since this is a one-tailed test (alternative hypothesis is μ < 10), we can use the t-distribution table, a t-distribution calculator, or statistical software to find the p-value.

Given the sample size of 18, the degrees of freedom for the t-distribution is 18 - 1 = 17.

Now, using a t-distribution calculator or statistical software, we can find the p-value:

p-value = P(T < -2.105, df = 17) ≈ 0.025

Therefore, the approximate p-value for this hypothesis test is 0.025.