Final answer:
The problem given is an example of using a one-sample t-test in statistics to determine if the mean summer rainfall is significantly different from the reported average. The findings suggest a rejection of the null hypothesis, indicating the mean rainfall is significantly less than the population mean, both at alpha levels of 0.05 and 0.01.
Step-by-step explanation:
The question deals with the concept of hypothesis testing in statistics, specifically employing a one-sample t-test to determine if there is a significant difference between the population mean and the sample mean of rainfall during the summer season. Given a sample mean of 7.42 inches of rainfall, a standard deviation of 1.3 inches, and a sample size of ten cities, we can test the null hypothesis that the population mean is 11.52 inches against the alternative hypothesis that it is lower.
Using an alpha level of 0.05, and assuming the population follows a normal distribution, the finding suggests that we should reject the null hypothesis, indicating that the mean amount of summer rainfall is significantly less than 11.52 inches. This conclusion remains the same even if the alpha level were adjusted to 0.01 because the p-value is almost 0, which is well below the 0.01 threshold, indicating strong evidence against the null hypothesis.