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

When the population variance is unknown and the sample size is 11, the Student's t-distribution is used to calculate the confidence interval for the mean. This accommodates the added uncertainty due to the small sample size and unknown population standard deviation.

Step-by-step explanation:

When conducting a study with 11 samples and the population variance is unknown, the distribution that is used to calculate the confidence interval is the Student's t-distribution. This distribution is appropriate when dealing with small sample sizes (typically less than 30) and when the population standard deviation is unknown. To calculate the confidence interval for the mean, one would use the sample mean, the sample standard deviation, and the appropriate t-value that corresponds to the desired confidence level and degrees of freedom (sample size minus one).

The calculation of the confidence interval would incorporate the variability of the sample data, and this interval would estimate the range within which the true population mean is likely to be found. For example, if we were looking to have a 90% confidence interval, about 90 percent of the confidence intervals constructed from repeated samples would contain the true population mean. The smaller the sample size, the wider the confidence interval, reflecting the increased uncertainty associated with the estimation.

Answer 2

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.