Question

ch 20* you are testing $h_{0}:\mu = 100$ against $h_{a}:\mu > 100$ based on an srs of 16 observations from a normal population. the t statistic is $t = 2.13$. the degrees of freedom for the t statistic are
16
17
15
question 7
1 pts
ch 20 which of the following is not a true statement about $s/\sqrt{n}$, the standard deviation of $\overline{x}$?
we need to know sigma when computing it.
we use it when we do not know sigma.
it is an approximation to the standard deviation of $\overline{x}$.
it estimates $\sigma/\sqrt{n}$.

Explanation:

Step1: Recall the formula for degrees of freedom in t - test

The formula for degrees of freedom in a one - sample t - test is \(df=n - 1\), where \(n\) is the sample size.

Step2: Substitute the value of \(n\)

Given \(n = 16\), then \(df=16-1\).

Step3: Calculate the degrees of freedom

\(df = 15\)

Step4: Analyze the statement about \(s/\sqrt{n}\)

• The formula \(s/\sqrt{n}\) is used when \(\sigma\) (population standard deviation) is unknown. \(s\) (sample standard deviation) is used to estimate \(\sigma\). So the statement “We need to know sigma when computing it” is False.

Answer:

For the first question: The degrees of freedom for the t - statistic is \(15\).
For the second question: The statement “We need to know sigma when computing it” is not a true statement about \(s/\sqrt{n}\).