Question

What can you conclude at the $5\%$ significance level ?

Short answer

We cannot reject the null hypothesis. There is enough evidence to conclude that the standard deviation is greater than $3.4$.

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 what can we conclude at the $5\%$significance level :

The $p-$value result was $0.0542$. Since we are given $\alpha =0.05$and

$0.05<0.0542=p$.

According to the information, we cannot reject null hypothesis. There is enough evidence to conclude that the standard deviation is greater than $3.4$.