would the null hypothesis that the 2000 mean hourly earnings of all workers was $16 be rejected at the 10% significance level in favor of the two-sided alternative? What about the null hypothesis that the mean was $15?

To determine if the null hypothesis can be rejected in favor of the two-sided alternative, we need to perform a hypothesis test and calculate the p-value. Here's how:

1. State the hypotheses:
- Null Hypothesis (H₀): The 2000 mean hourly earnings of all workers is $16.
- Alternative Hypothesis (H₁): The 2000 mean hourly earnings of all workers is not equal to $16 (two-sided).

2. Collect a random sample of 2000 hourly earnings data from the target population of workers in 2000.

3. Calculate the sample mean (x̄) and the sample standard deviation (s) from the collected data.

4. Choose an appropriate statistical test. Since you have a large sample size (n = 2000) and the population standard deviation is typically unknown in this scenario, we can use the z-test.

5. Calculate the test statistic (z-score). The formula is:
z = (x̄ - μ) / (s / √n)
where:
- x̄ is the sample mean
- μ is the hypothesized mean under the null hypothesis (in this case, $16)
- s is the sample standard deviation
- n is the sample size (2000)

6. Determine the p-value associated with the obtained z-score. You can look up the p-value from a z-table or use a statistical software or calculator.

7. Compare the p-value with the significance level (α). In this case, the significance level is 10% or 0.10. If the p-value is less than the significance level, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

Now, let's address each scenario separately:

For the null hypothesis that the mean hourly earnings was $16, follow the steps above to calculate the z-score and obtain the p-value. If the p-value is less than 0.10, you can reject the null hypothesis in favor of the two-sided alternative.

For the null hypothesis that the mean hourly earnings was $15, repeat the same steps but use the new hypothesized mean of $15 instead. Calculate the z-score and obtain the p-value. Again, if the p-value is less than 0.10, you can reject the null hypothesis in favor of the two-sided alternative.

Remember, the p-value represents the probability of observing a test statistic as extreme as the one obtained, assuming the null hypothesis is true.