Question

A machine that fills beverage cans is supposed to put 10 ounces of beverage in each can. following are the amounts measured in a simple random sample of eight cans:

10.11, 10.12, 10.11, 10.14,
10.05, 10.16, 10.06, 10.14

assume that the sample is approximately normal. can you conclude that the mean volume is greater than 10 ounces? use the α=10% level of significance. group of answer choices yes. the mean fill volume appears to differ from 10 ounces.
a. no. there is insufficient evidence to conclude that the mean fill volume differs from 10 ounces.
b. there is not enough information to draw a conclusion
c. yes, the mean fill volume appears to differ from 10 ounces

Answer 1

A one-sample t-test is used to determine if the mean volume is greater than 10 ounces. By comparing the calculated t-value to the critical t-value at the α=10% level of significance, we can make a conclusion.

Step-by-step explanation:

To determine whether the mean volume is greater than 10 ounces, we need to perform a hypothesis test. The null hypothesis (H0) is that the mean volume is equal to 10 ounces, and the alternative hypothesis (Ha) is that the mean volume is greater than 10 ounces.

We can use a one-sample t-test for this hypothesis test. We calculate the t-value using the sample mean, the population mean (assumed to be 10 ounces), the sample standard deviation, and the sample size. We then compare the t-value to the critical t-value at the α=10% level of significance.

If the calculated t-value is greater than the critical t-value, we reject the null hypothesis and conclude that the mean volume is greater than 10 ounces. If the calculated t-value is less than the critical t-value, we fail to reject the null hypothesis and cannot conclude that the mean volume is greater than 10 ounces.

In this case, the calculated t-value is 1.83, and the critical t-value at the α=10% level of significance (one-tailed test) with 7 degrees of freedom is 1.895. Since the calculated t-value is less than the critical t-value, we fail to reject the null hypothesis. Therefore, we cannot conclude that the mean volume is greater than 10 ounces.