Question

a sample mean, sample size, and sample standard deviation are provided below. use the one - mean t - test to perform the required hypothesis test at the 10% significance level.
\\( \overline { x } = 26, s = 9, n = 32, h _ { 0 } : \mu = 21, h _ { a } : \mu > 21 \\)
click here to view a partial table of values of \\( t _ { \alpha } \\).
the test statistic is \\( t = 3.14 \\).
(round to two decimal places as needed.)
the p - value is

Explanation:

Step1: Determine the degrees of freedom

The degrees of freedom \(df=n - 1\). Given \(n = 32\), so \(df=32-1 = 31\)

Step2: Use the t - distribution table or calculator

We know the test statistic \(t = 3.14\) and it is a right - tailed test (\(H_{a}:\mu>21\)).
Using a t - distribution calculator with \(df = 31\) and \(t=3.14\), we find the P - value.
Using a calculator (e.g., in R: 1 - pt(3.14,31)), the P - value is approximately \(0.002\)

Answer:

The P - value is \(0.002\)