To help with this problem, let’s analyze the details and address Part 1: defining the hypotheses and identifying the type of test.

1. Null Hypothesis $H_0$: The mean number of cigarettes smoked per day is equal to 32 ($\mu = 32$).
2. Alternative Hypothesis $H_1$: The mean number of cigarettes smoked per day is less than 32 ($\mu < 32$), since the claim is that 32 is "too high."
3. This is a left-tailed test since the alternative hypothesis suggests a value lower than 32.

Would you like further explanation on setting up the hypotheses or calculating the test statistic? Here are some follow-up questions:

1. How do you calculate the test statistic in this scenario?
2. What is the critical value for a left-tailed test at $\alpha = 0.01$?
3. How do you use a TI-83 calculator to find the p-value?
4. What assumptions must be met for this hypothesis test?
5. Why is the population distribution important in this context?

Tip: Always state your null and alternative hypotheses clearly to avoid confusion when performing statistical tests.