Final answer:
The question is about using hypothesis testing to determine if the mean summer rainfall in ten northeastern US cities is significantly less than the reported average, and interpreting data regarding rainfall amounts from a table.
Step-by-step explanation:
The correct answer is option Mathematics, and this question pertains to statistical methods used in analyzing rainfall data, particularly hypothesis testing and interpreting data distributions.
In the context of hypothesis testing, we are asked to perform a test to evaluate whether the mean rainfall in ten cities in the northeastern United States is significantly different from the reported average at two significance levels, α = 0.05 and α = 0.01.
To answer this, we would calculate the test statistic using the sample mean, sample standard deviation, and the number of cities. Then, we'd compare the test statistic to a critical value from the standard normal distribution to decide if we can reject the null hypothesis that the mean rainfall is at least 11.52 inches.
For the second part, interpreting data from a table (Table 1.16) and finding percentages or fractions of towns with rainfall within certain ranges requires understanding of normal distribution properties and could involve using a Z-score table or similar statistical tools.
The correct answer is option B (58.2 ± 0.1). To calculate the error estimation, we need to find 10% of the average rainfall. The average rainfall is the sum of the rainfall measurements divided by the number of measurements. So, the average rainfall is (89 + 54 + 45 + 41 + 55) / 5 = 284 / 5 = 56.8 inches.
Now, to find 10% of the average rainfall, we multiply it by 0.1. Therefore, the error estimation should not exceed 10% of 56.8 inches, which is 5.68 inches.