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
[tex]df =10[/tex]
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.
