Question

What is the test statistic?

Short answer

The value of the test statistic is$42.17$.

Step-by-step solution

Given Information

The average waiting time in a doctor’s office varies. The standard deviation of waiting times in a doctor’s office is $3.4$ minutes. A random sample of $30$ patients in the doctor’s office has a standard deviation of waiting times of $4.1$ minutes.

Explanation

We have to find the test statistic:

Here, we observed that

$n=30$

$s=4.1$

$\sigma =3.4$

Let's find the null hypothesis and alternative hypothesis

Null hypothesis: $H_0:{\sigma }^2={3.4}^2$

Alternative hypothesis: $H_a:{\sigma }^2>{3.4}^2$

Then, compute the degrees of freedom:

$n-1$

$=30-1$

$=29$

We can compute the test statistics by using the given formula

localid="1648703739753" $Teststatistic=\frac{(n-1)s^2}{{\sigma }^2}$

$=\frac{(29-1){(4.1)}^2}{{(3.4)}^2}$

$=\frac{29\times 16.81}{11.56}$

$=42.17$