The t- score for a sampling distribution is 2
The t-score is the number of standard deviations from the mean in the t-distribution.
The upper and lower bounds of a confidence interval when the data are approximately normally distributed.
T-scores and confidence intervals
Confidence intervals use t-scores to calculate the upper and lower bounds of the prediction interval. The t-score used to generate the upper and lower bounds is also known as the critical t or t* value.
The t- distribution is given by
t=(x – μ) / (S / √n)
t = T – Distribution
x = sample mean
μ = population mean
S = standard deviation
n = Sample size
It is given that sampling distribution mean of 10.5, a standard deviation of 1.5, and a size of 36 drawn from a population that has a mean of 10.
We need to find the t-score for sampling distribution
t=(x – μ) / (S / √n)
Here, x= 10.5 , μ= 10, S=1.5, n=36
t = (10.5 - 10)/ (1.5 /√36)
t= 2
Hence the value of t-score is 2
Learn more about t-score here
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