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# One-Sample $t$ Test Calculator

• The $t$ procedures assume that our data come from an SRS and will give trustworthy conclusions only if this condition is met.

• If your sample size is less than $15,$ the $t$ procedures yield trustworthy conclusions only if you can reasonably assume that your data comes from a normal distribution, that is, if the distribution appears to be symmetric with one peak and no outliers. If your data are obviously skewed or if there are any outliers, it is not advisable to use the $t$ procedures. Non-parametric or Bootstrap methods may be more advisable: try the Wilcoxon Signed Rank Test for a Population Median or the Single Parameter Bootstrap Test of Significance for either a population mean or median.

• If your sample size is $15$ or larger, the $t$ procedures can be trusted if there are no outliers and the distribution is not obviously skewed.

• If your sample size is $40$ or larger, you may use $t$ procedures even if your distribution appears to be skewed.
 Data Sample data goes here (enter numbers in columns): Sample Mean: $\bar{x}=$ Sample Standard Deviation: $s=$ Sample Size: $n=$ Null Hypothesis: $H_0: \mu=\mu_0=$ Alternative Hypothesis: $H_a:\mu$ $\neq$ $<$ $>$ $\mu_0$ Level of Significance: $\alpha=$ 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005 Use Summary Statistics:

 Sample Size: $n=$ Degrees of Freedom: $df=n-1=$ Sample Mean: $\overline{x}=$ Sample Standard Deviation: $s=$ Critical $t$ Value: $t^{*}=$ $t$ statistic: $t=$ $p\mbox{-value}$: