Question

In a study using 11 samples, and in which the population variance is unknown,the distribution that should be used to calculate the confidence interval is?

Answer 1

Answer:

The correct answer is option (C)

a t distribution with 10 degrees of freedom"

Step-by-step explanation:

CHECK THE COMPLETE QUESTION BELOW;

In a study using 11 samples, and in which the population variance is unknown,the distribution that should be used to calculate the confidence interval is?

A) a standard normal distribution.

B) a t distribution with 12 degrees of freedom.

C) a t distribution with 10 degrees of freedom.

D) a t distribution with 9 degrees of fredom

EXPLANATION;

In a study using 11 samples,

n= 11

Since population variance is unknown so the population standard deviation is unknown too.

The standard deviation is the square root of the variance

σX = σ2

since,

* the the population standard deviation is unknown and at the same time

*the sample size n is less than 30

Therefore, the T distribution with degrees of freedom (df) must be used

df = n-1

df = 11-1

$df =10$

The t distribution also known as Student’s t-distribution is referred to as a probability distribution that allow the population parameters to be estimated when the sample size is small and/or when the population variance is unknown.

Therefore, the correct answer is a t distribution with 10 degrees of freedom.