Point of Interest:
Distribution & Estimation?
A randaom sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were:
3.087, 3.131, 3.241, 3.241, 3.270, 3.353, 3.400, 3.411, 3.437, 3.477
How do I construct a 90 percent confidence interval for the true mean weight?
Confidence intervals are used to find a region in which we are 100 * ( 1 - α )% confident the true value of the parameter is in the interval.
In order for the Confidence Interval to be valid you must have data from a normal distribution, at least if you are using the method here. If you do not have normal data then this type of confidence interval is not valid.
To clear up the notation I will use here. "t" is the test statistic and "t_(n-1)" is a Student t random variable with n - 1 degrees of freedom, e.g. a Student t random variable with 18 degrees of freedom is denoted as t_18.
For small sample confidence intervals about the mean you have:
xBar ± t * sx / sqrt(n)
where xBar is the sample mean
t is the t - score with n - 1 degrees of freedom such that α% of the data in the tails, i.e., P( |t_(n-1)| > t) = α
sx is the sample standard deviation
n is the sample size
The sample mean xbar = 3.3048
The sample standard deviation sx = 0.1319889
The sample size n = 10
The t score for a 0.9 confidence interval is the t score such that 0.05 is in each tail.
t = 1.833113
The confidence interval is:
( xbar - t * sx / sqrt( n ) , xbar + t * sx / sqrt( n ) )
( 3.228289 , 3.381311 )
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