### Using the $C$% confidence interval for $\mu$ to perform paired sample $t$ test

Be sure you understand the theory behind confidence intervals and significance tests, before trying to understand the explanation behind the 'explain' button.

Two sided test |
If $\mu_0$ is not in the $C$% confidence interval, the sample mean of the difference scores is significantly different from $\mu_0$ at significance level $\alpha = 1 - C/100$. For instance, if $\mu_0$ is not in the $95$% confidence interval, the sample mean of the difference scores is significantly different from $\mu_0$ at significance level $\alpha = 1 - 95/100 = .05$. Explain |

Right sided test |
If $\mu_0$ is not in the $C$% confidence interval and the sample mean of the difference scores is larger than $\mu_0$, the sample mean of the difference scores is significantly larger than $\mu_0$ at significance level $\alpha = \frac{1 \, - \, C/100}{2}$. For instance, if $\mu_0$ is not in the $90$% confidence interval and the sample mean of the difference scores is larger than $\mu_0$, the sample mean of the difference scores is significantly larger than $\mu_0$ at significance level $\alpha = \frac{1 \,-\, 90/100}{2} = .05$. Explain |

Left sided test |
If $\mu_0$ is not in the $C$% confidence interval and the sample mean of the difference scores is smaller than $\mu_0$, the sample mean of the difference scores is significantly smaller than $\mu_0$ at significance level $\alpha = \frac{1 \,-\, C/100}{2}$. For instance, if $\mu_0$ is not in the $90$% confidence interval and the sample mean of the difference scores is smaller than $\mu_0$, the sample mean of the difference scores is significantly smaller than $\mu_0$ at significance level $\alpha = \frac{1 \,-\, 90/100}{2} = .05$. Explain |