Question

Suppose we compute a two-sided 99% t-interval for the mean y, and we find that 30.0 does not lie inside the interval. Consider a t-test of Ho: u = 30.0 versus HA: " + 30.0 True or False: From this information, we can determine whether or not the t-test rejects Ho at significance level a = 0.04.

Answer 1

If we compute two-sided 99% t-interval for $\mu$ and we find that 30.0 does not lie inside the interval. Then we can reject the null hypothesis of the t-test

H₀:$\mu$=30.0 versus H_A:$\mu$$\neq$30.0

Since 99% t-interval contains the 96% t-interval. So we can conclude that 30.0 in not in the 96% t-interval for $\mu$ ​​​​​​.

Thus we can reject the null hypothesis of this test

H₀:$\mu$=30.0 versus H_A:$\mu$$\neq$30.0 at significance level $\alpha$ =0.04

So the statement "From this information, we can determine whether or not the t-test rejects H₀ at significance level $\alpha$ =0.04" is ​​​​​​​true.