Question

Bottles of grape soda are assumed to contain 300 milliliters of soda. 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 nine randomly selected bottles from one day of production. The results are 298.7, 299.4, 301.9, 301.3, 300.9, 300.6, 301.7, 300.4, and 301.5 milliliters. Do these data provide convincing evidence at α = 0.05 that the mean amount of soda in all the bottles filled that day differs from the target value of 300 milliliters? (4 points)
Group of answer choices

Because the p-value of 0.0414 is greater than the significance level of 0.05, we fail to reject the null hypothesis. We conclude the data provide convincing evidence that the mean amount of soda in all the bottles filled that day does not differ from the target value of 300 milliliters.

Because the p-value of 0.0414 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 soda in all the bottles filled that day differs from the target value of 300 milliliters.

Because the p-value of 0.0828 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 soda in all the bottles filled that day differs from the target value of 300 milliliters.

Because the p-value of 0.0828 is greater than the significance level of 0.05, we fail to reject the null hypothesis. We conclude the data provide convincing evidence that the mean amount of soda in all the bottles filled that day does not differ from the target value of 300 milliliters.

Because the p-value of 1.9819 is greater than the significance level of 0.05, we fail to reject the null hypothesis. We conclude the data provide convincing evidence that the mean amount of soda in all the bottles filled that day does not differ from the target value of 300 milliliters.

Answer 1

Answer:

Because the p-value of 0.0828 is greater than the significance level of 0.05, we fail to reject the null hypothesis. We conclude the data provide convincing evidence that the mean amount of soda in all the bottles filled that day does not differ from the target value of 300 milliliters.

Step-by-step explanation:

The null hypothesis is that the sample mean does not differ from the population mean.

If p < α, we reject the null hypothesis.

If p > α, we do not reject the null hypothesis.

p values are between 0 and 1.