Final answer:
To determine if the data supports the claim at the 1% level, we need to conduct a hypothesis test. The t-value is 0, which is not beyond the critical values, so we fail to reject the null hypothesis. Therefore, the data does not support the claim at the 1% level.
Step-by-step explanation:
To determine if the data supports the claim at the 1% level, we need to conduct a hypothesis test. The null hypothesis (H0) is that the population mean is 5.1, while the alternative hypothesis (Ha) is that the population mean is different from 5.1. We will use a t-test since the population standard deviation is not known. The critical value for a two-tailed test at a 1% level of significance with n-1 degrees of freedom (where n is the sample size) is approximately ±2.68.
We calculate the t-value: t = (sample mean - population mean) / (sample standard deviation / √sample size). t = (5.1 - 5.1) / (1.2 / √n) = 0 / (1.2 / √n) = 0. Since the t-value is 0, it is not beyond the critical values of ±2.68, so we fail to reject the null hypothesis. Therefore, the data does not support the claim at the 1% level.