Question

Concept only no math needed.

You wish to estimate the average weight of a mouse. You obtain 10 mice, sampled uniformly at random and with replacement from the mouse population. Their weights are 21; 23; 27; 19; 17; 18; 20; 15; 17; 22 grams respectively. Notice there are too few mice to use a normal model.

What distribution would you use instead of the normal distribution in order to find confidence intervals? State the name of the distribution and the number of degrees of freedom.

Answer 1

Solution =

Given, the 10 sample of mice weights in grams,

21; 23; 27; 19; 17; 18; 20; 15; 17; 22

n = 10

In the case that the population standard deviation \sigmaσ is not known,

We use instead the sample standard deviation s. Please type the sample mean, the sample standard deviation, the sample size and the confidence level,

A confidence interval for the population mean \muμ when the population standard deviation is not known  the value t_{\alpha/2, n-1}tα/2,n−1​ is the critical t-value associated with the specified confidence level and the number of degrees of freedom df = n -1.

We also using a t-distribution use instead of the normal distribution in order to find confidence intervals.

using a t-distribution the critical t-value associated with the specified confidence level and the number of degrees of freedom df = n -1 = 10-1 = 9

Degrees of freedom = 9