t-Distributions

T-distributions represent a critical aspect of probability distribution frequently employed in the field of statistics. They bear similarity to normal distributions, with the key difference being their thicker tails, which accommodates greater variability. The significance of t-distributions becomes more evident when we work with smaller sample sizes or when the population standard deviations are not known.

Finding a t-Value for a Confidence Level

A researcher is interested in estimating the population mean from a sample of size 20 with a sample mean of 30 and a sample standard deviation of 4. What is the t-value for a 95% confidence level?

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Finding the Critical t-Value

Complete parts (a) through (c) below. (a) Determine the critical value(s) for a right-tailed test of a population mean at the $\alpha=0.10$ level of significance with 20 degrees of freedom. (b) Determine the critical value(s) for a left-tailed test of a population mean at the $\alpha=0.05$ level of significance based on a sample size of $n=15$. (c) Determine the critical value(s) for a two-tailed test of a population mean at the $\alpha=0.01$ level of significance based on a sample size of $n=11$. Click here to view the t-Distribution Area in Right Tail. (a) $t_{\text {crit }}=\square \square$ (Round to three decimal places as needed.)

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t-Distributions

Finding a t-Value for a Confidence Level

Finding the Critical t-Value

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