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Confidence Level and $1$-sided Significance Testing

APSTAT-X4JEUW

A one sample $t$-test for was used to conduct a test of the null hypotheses:

$${ H }_{ 0 }:\mu =28$$
$${ H }_{ a }:\mu <28$$

The $p$-value was $0.006$. A confidence interval for $\mu$ is to be constructed.

Of the following, which is the largest level of confidence for which the confidence interval will NOT contain $28$?

A

$95\%$

B

$96\%$

C

$97\%$

D

$98\%$

E

$99\%$