A business professor was previously interested in how much cash people carried with them when they left the house. Over years, the professor established that the population mean was 42 dollars. More recently, he was interested in whether or not the value has changed over time, so he collected data on a small sample. Here are the data: 51, 43, 36, 15, 4, 41, 29, 19, 10, 44, 49, 38, 29, 40, 16. Is there evidence that this sample was drawn from a population with a mean different from 42 dollars? Complete the seven steps of hypothesis testing for this problem. Complete Step 5 by hand. Be sure to show your work for any calculations. The problem is worth 5 total points, 2 points for step 5 and of a point for steps 1-4 and 6-7. (Adapted from Statistics for the Behavioral Sciences by Thorne and Giesen)

Step 1.

Step 2.

Step 3.

Step 4.

Step 5. t = __________ (attach work)

Step 6. Circle your decision below:

1. Reject H₀
2. Fail to reject H₀

Step 7. Circle your conclusion below:

1. The average amount of cash carried when leaving the house is not different than in previous years.
2. The average amount of cash carried when leaving the house is significantly greater than in previous years.
3. The average amount of cash carried when leaving the house is significantly lower than in previous years.