Bottles of purified water are assumed to contain 250 milliliters of water. There is some variation from bottle to bottle because the filling machine is not perfectly precise. Usually, the distribution of the contents is approximately Normal. An inspector measures the contents of eight randomly selected bottles from one day of production. The results are 249.3, 250.2, 251.0, 248.4, 249.7, 247.3, 249.4, and 251.5 milliliters. Do these data provide convincing evidence at α = 0.05 that the mean amount of water in all the bottles filled that day differs from the target value of 250 milliliters? Because the p-value of 0.4304 is greater than the significance level of 0.05, we fail to reject the null hypothesis. We conclude the data provide insufficient evidence that the mean amount of water in all the bottles filled that day differs from the target value of 250 milliliters.

Because the p-value of 0.4304 is greater than the significance level of 0.05, we reject the null hypothesis. We conclude the data provide convincing evidence that the mean amount of water in all the bottles filled that day differs from the target value of 250 milliliters.

Because the p-value of 0.2152 is greater than the significance level of 0.05, we fail to reject the null hypothesis. We conclude the data provide insufficient evidence that the mean amount of water in all the bottles filled that day differs from the target value of 250 milliliters.

Because the p-value of 0.2152 is greater than the significance level of 0.05, we reject the null hypothesis. We conclude the data provide convincing evidence that the mean amount of water in all the bottles filled that day differs from the target value of 250 milliliters.

Because the p-value of 0.8367 is greater than the significance level of 0.05, we fail to reject the null hypothesis. We conclude the data provide insufficient evidence that the mean amount of water in all the bottles filled that day differs from the target value of 250 milliliters.