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2 weeks ago
Before you took this course, you probably heard many stories about Statistics courses. Oftentimes parents of students have had bad experiences with Statistics courses and pass on their anxieties to their children. To test whether actually taking AP* Statistics decreases students' anxieties about statistics, an AP* statistics instructor gave a test to rate student anxiety at the beginning and end of his course. Anxiety levels were measured on a scale of 0-10. Here are the data for 16 randomly chosen students from a class of 180 students:




Do the data indicate that anxiety levels about Statistics decreases after students take AP* Statistics? Test an appropriate hypothesis and state your conclusion.
Textbook 

Stats: Modeling the World


Edition: 4th
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2 weeks ago
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Let d = Post-course anxiety level - Pre-course anxiety level.
H0: μd = 0 The mean difference in the anxiety levels is zero.
HA: μd < 0 The mean difference in the anxiety levels is less than zero.
* Paired data: The data are paired because they are measurements on the same individuals both before and after the intro stats course.
* Independence: The anxiety level of any student is independent of the anxiety level of any other student, so the differences are independent.
* Randomization: We are told this is a random sample from the class.
* 10% condition: Our sample of 16 students is less than 10% of the students who take AP* Statistics.
* Nearly Normal condition: The histogram of the differences is unimodal and roughly symmetric.

Under these conditions the sampling distribution of the differences can be modeled by a Student's t-model with (n - 1) = 15 degrees of freedom, and we will use a paired t-test.
We find from the data: n = 16 , = -1.125 , and sd = 1.1475.
We estimate the standard deviation of using: SE() = = = 0.287.
t15 = = = -3.92, so our P-value is P(t15 < -3.92) = 0.0007
With a P-value this small, we can reject the null hypothesis. We have strong evidence that taking AP* Statistics reduces the anxiety level of students.
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