Question

The standard deviation of heights for students in a school is $0.81$. A random sample of $50$students is taken, and the standard deviation of heights of the sample is $0.96$. A researcher in charge of the study believes the standard deviation of heights for the school is greater than $0.81$.

To find the value of$df$.

Short answer

The number of degrees of freedom is$df=49$.

Step-by-step solution

Given Information

A random sample of $50$ students is taken, and the standard deviation of the heights of the sample is $0.96$.

Explanation

We have to find the value of degrees of freedom:

A random sample has $n=50$students.

Therefore, the number of degrees is :

$n-1$

$=50-1$

$=49$

The value of degrees of freedom is$df=49$