Question

A food truck operator has traditionally sold 75 bowls of noodle soup each day. He moves to a new location and after a week sees that he has averaged 85 bowls of noodle soup sales each day. He runs a one-sided hypothesis test to determine if his daily sales at the new location have increased. The p-value of the test is 0.031. How should he interpret the p-value?

There is a 3.1% chance that the true mean of soup sales at the new location is 85 bowls a day.

There is a 96.9% chance that the true mean of soup sales at the new location is greater than 75 bowls a day.

There is a 96.9% chance that the sample mean of soup sales at the new location is 85 bowls a day.

There is a 3.1% chance of obtaining a sample with a mean of 85 or higher assuming that the true mean sales at the new location is still equal to or less than 75 bowls a day.

There is a 96.9% chance that the true mean of soup sales at the new location is within 3.1 bowls of 85 bowls a day.

Answer 1

P values evaluate how well the sample data support the devil’s advocate argument that the null hypothesis is true. It measures how compatible your data are with the null hypothesis. How likely is the effect observed in your sample data if the null hypothesis is true?

Assuming that the no difference in mean, you’d obtain the observed difference or more in 3.1% of studies due to random sampling error.

Answer:- There is a 3.1% chance of obtaining a sample with a mean of 85 or higher assuming that the true mean sales at the new location are still equal to or less than 75 bowls a day.