The appropriate t-multiplier for a 95% confidence interval for the mean μ is t(0.025,14) = 2.15.
Given:
The t-multiplier for a 95% confidence interval for a population mean, using a well-behaved sample of size 14.
It is the 97.5%-quantile of the t-distribution with 14 degrees of freedom.
In the figure the dashed line shows the value such that the yellow shaded area has size 0.975: the 97.5%-quantile is the value such that 97.5% of the probability mass is to the left of it and the rest to the right.
so t - multiplier = 2.15.
Therefore the appropriate t-multiplier for a 95% confidence interval for the mean μ is t(0.025,14) = 2.15.
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