How to solve...

Mahesh, what are your ideas for how to solve?

I like to think about the problem from a very broad perspective first before reaching for the 'tools' and tests.
I agree, you should do individual T-tests for each case. The first being you want to know if the traffic is at least 300 during peak hours. The second being you want it to be at least 150 during lean hours. But since you only care about it being higher, not lower, doing a one-sided, one-tailed, test is appropriate.

Before you conduct these tests, first agree upon a risk level, or alpha. Many people use 0.05, but choose something that makes sense for the problem at hand. The alpha risk is the risk that the test tells you there is a difference between the observed data and null hypothesis when there really isn't.

The T-Test will give you a probability of observing the data given a certain null hypothesis. In the first case, the null hypothesis is that the true average is 300 cars per hour. Once you conduct the 1-sample 1-sided T-test, you will get a p-value. For example if the p-value is .15, that means that there is a 15% chance you observed this data if the true average is 300. If you choose an alpha of 0.10, you would not have sufficient evidence to reject the null hypothesis. Meaning, there is not enough evidence to say the true average is significantly larger than 300. Good luck.