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you are employed to check quality control at a company that bottles drinks. cans of drink should contain 8.0 oz of drink. you remove a small random sample of cans and measure the actual amount of drink in them and find there is an average of 7.91 oz with a standard deviation of 0.17 oz. which statistical test would be best to determine if the amount of drink in cans are signficantly less than the target 8.0 oz?

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Final answer:

The one-sample t-test is the statistical test needed to determine if the average measured amount of drink in the cans, which is 7.91 oz, is significantly less than the target of 8.0 oz. This should be a one-tailed test since we are only interested in whether the sample mean is less than the target.

Step-by-step explanation:

The appropriate statistical test for determining if the amount of drink in cans is significantly less than the target 8.0 oz is a one-sample t-test. This test compares the sample mean to the known population mean to see if there is a statistically significant difference between them. Since we are checking if the sample average of 7.91 oz with a standard deviation of 0.17 oz is less than the target, it will be a one-tailed test. Additionally, we presumably do not know the population standard deviation, making the t-test rather than the z-test the correct choice.

To conduct a one-sample t-test, we first formulate the null hypothesis (H0) that the average amount of drink in the cans is equivalent to the target amount (8.0 oz), and the alternative hypothesis (H1) that the average amount is less than the target. We then calculate the t-statistic using the sample mean, sample standard deviation, and sample size. The t-statistic is compared to a t-distribution to find the p-value. If the p-value is below a predetermined level of significance (commonly 0.05), we reject the null hypothesis and conclude that the cans contain significantly less drink than the target amount.

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