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?

The options

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

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

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

D) 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.+9

Answer 1

we know that the p value represents the probability of obtaining a given event

Given event means the condition that we wish to see using the alternate hypothesis, given the condition of null hypothesis

so, a p value of 3.1% means that we have 3.1% probability of obtaining mean of 85 or higher (alternate hypothesis condition), given that the null hypothesis condition is valid .

therefore, option D is matching with our explanation

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.