Question

complete the following analysis
mean 26.44 mean 26.19
standard deviation 9.9 standard deviation 9.68
sample size 16 sample size 16
calculated t value 0.07
degrees of freedom 30
critical value 2.04
what is your conclusion?
absolute value of t is less than the critical value.
therefore the result statistically significant.
therefore i will the null hypothesis.

Explanation:

Step1: Compare t - value and critical value

We are given that the calculated \(t\) - value \(t = 0.07\) and the critical value \(t_{critical}=2.04\). The absolute value of the calculated \(t\) - value is \(|t|=|0.07| = 0.07\). Since \(0.07<2.04\), the absolute value of \(t\) is less than the critical value.

Step2: Determine statistical significance

In a \(t\) - test, if \(|t|

Step3: Make a decision about the null hypothesis

When the result is not statistically significant, we fail to reject the null hypothesis. We do not have enough evidence from the sample data to support the alternative hypothesis.

Answer:

The absolute value of \(t\) is less than the critical value. Therefore the result is not statistically significant. Therefore I will fail to reject the null hypothesis.