Answer: Yes, there is convincing evidence at the 0.01 level that more than 10% of households in this town still have their Christmas lights up on February 1st.
Explanation: To answer this question, we can conduct a hypothesis test. The null hypothesis is that 10% of households still have their Christmas lights up, and the alternative hypothesis is that more than 10% of households still have their lights up.
The test statistic can be calculated using the formula:
z = (x - mu) / (sigma / sqrt(n))
where x is the sample proportion (15/100 = 0.15), mu is the population proportion (0.10), sigma is the standard deviation of the population proportion (sqrt(0.10 * 0.90 / 100) = 0.039), and n is the sample size (100).
z = (0.15 - 0.10) / (0.039 / sqrt(100)) = 2.33
Next, we find the p-value associated with this test statistic. A p-value is the probability of observing a test statistic as extreme or more extreme than the one calculated if the null hypothesis were true. A p-value less than 0.01 would indicate strong evidence against the null hypothesis.
Using a standard normal table, the p-value for a z-score of 2.33 is 0.009, which is less than 0.01.
Therefore, there is convincing evidence at the 0.01 level that more than 10% of households in this town still have their Christmas lights up on February 1st.