91Ó°ÊÓ

We are given following information:

Mean of responses = $7.9$

Standard deviation =$2.1$

Remember that the null is identical to the hypothesized value while constructing the null and alternative.

The sample mean is $7.9$, which differs from the hypothesized value. So the hypothesized value is $9$.

$⇒$Null Hypothesis $H_0:\mathrm{μ}=9$

Whether the test is a left or right tail, or both, is determined by the alternative hypothesis.

We're curious if kids are receiving less sleep than we will go for the left tail test. It would be a right tail test if we were interested in pupils sleeping too much. Because the researchers are deliberately looking for too little sleep. So researchers will go for left tail test and alternative hypothesis will be less than null hypothesis.

$⇒$Alternative Hypothesis $H_a:\mathrm{μ}<9$

Hence, option (d) is correct.