Question

Tracy bought a coffee express machine that made one specific kind of coffee and in only one size. The coffee machine was designed to dispense 200 mL of coffee per serving. Tracy suspects that the machine is dispensing too much coffee than intended. She decides to take a sample of 50 drinks to see if the average amount is significantly greater than 200 mL. Write an appropriate hypotheses for the significance test? 4

Answer 1

Tracy should set up a null hypothesis stating the mean volume dispensed is 200 mL and an alternative hypothesis stating the mean volume is greater than 200 mL to perform a significance test.

Step-by-step explanation:

For Tracy's situation where she suspects her coffee express machine is dispensing more than the intended 200 mL of coffee per serving, the appropriate hypotheses for a significance test would be:

• Null Hypothesis (H0): The mean volume dispensed is equal to 200 mL, which can be written as µ = 200 mL.
• Alternative Hypothesis (H1): The mean volume dispensed is greater than 200 mL, which can be written as µ > 200 mL.

These hypotheses set up the basis for conducting a one-sample t-test or a z-test, depending on the known or unknown population standard deviation. Since Tracy is checking for a volume greater than the intended amount, it's a one-tailed test. She will collect the sample data and use statistical software or methods to determine if there is significant evidence to reject the null hypothesis.