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Hypothesis Testing with R
P-Values

You know that a hypothesis test is used to determine the validity of a null hypothesis. Once again, the null hypothesis states that there is no actual difference between the two populations of data. But what result does a hypothesis test actually return, and how can you interpret it?

A hypothesis test returns a few numeric measures, most of which are out of the scope of this introductory lesson. Here we will focus on one: p-values. P-values help determine how confident you can be in validating the null hypothesis. In this context, a p-value is the probability that, assuming the null hypothesis is true, you would see at least such a difference in the sample means of your data.

Consider the experiment on history and chemistry majors and their interest in volleball from a previous exercise:

• Null Hypothesis: `"History and chemistry students are interested in volleyball at the same rates"`
• Experiment Sample Means: `34%` of history majors and `39%` of chemistry majors sign up for the volleyball class

A hypothesis test on the experiment data that returns a p-value of `0.04` would indicate that, assuming the null hypothesis is true and there is no difference in preference for volleyball between all history and chemistry majors, you would see at least such a difference in sample mean (`39%` - `34%` = `5%`) only `4%` of the time due to sampling error.

Essentially, if you ran this same experiment `100` times, you would expect to see as large a difference in the sample means only `4` times given the assumption that there is no actual difference between the populations (i.e. they have the same mean).

Seems like a really small probability, right? Are you thinking about rejecting the null hypothesis you originally stated?

Instructions

1.

You are big fan of apples, so you gather `10` green and `10` red apples to compare their weights. The green apples average `150` grams in weight, and the red apples average `160` grams in weight.

You run a hypothesis test to see if there is a significant difference in the weight of green and red apples. The test returns a p-value of `0.2`. Which statement (`st_1`, `st_2`, `st_3`, or `st_4`) indicates how this p-value can be interpreted?

Update the value of `interpretation` with the string `"st_1"`, `"st_2"`, `"st_3"`, or `"st_4"` depending on your answer.

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