Question

determine the critical value for a one tailed test with a sample size of 17. you do not know the population standard deviation, and are using a level of significance of 0.02. use three decimal places for your answer.

Explanation:

Step1: Determine the degrees of freedom

The degrees of freedom \(df=n - 1\), where \(n = 17\). So \(df=17-1 = 16\).

Step2: Find the critical value

Since it is a one - tailed test with \(\alpha=0.02\) and we use the t - distribution (because the population standard deviation is unknown), we look up the value in the t - distribution table.
For \(df = 16\) and \(\alpha=0.02\) (one - tailed), the critical value \(t\) is obtained from the t - distribution. Using a t - table or a calculator with a t - distribution function (e.g., in R: qt(0.98,16) or in Excel: T.INV(0.98,16)), we get \(t = 2.224\).

Answer:

\(2.224\)