A statistician wants to determine if there is a significant difference in GPA be

Question

A statistician wants to determine if there is a significant difference in GPA between the Hogwarts houses Slytherin and Gryffindor. She doesn’t have access to the population means or population standard deviations for each house. For each situation below, determine which type of error (if any) was made in the study, using the word bank provided. Please select only one type of error for each.

Word Bank:

-Running Test on Entire Population -Data snooping

-Violation of Conditions for a test            -Biased Sampling Method

-No Mistake was made -Incorrect Interpretation

A) She uses a huge spreadsheet with all of the GPAs of everybody in each house, and performs a two-sample z-test on this data to test for significantly different means.

B) She takes a simple random sample of 70 individuals from each house. She calculates the mean GPA for each house and runs a two-sample z test on this data.

C) She takes a simple random sample of 100 Gryffindor students and a simple random sample 25 Slytherin students. She performs a two-sample z-test on the data and concludes there is a difference in means.

D) She examines the sample data before performing the test, sees that the Gryffindors have higher GPAs than the Slytherins, and decides that the alternative hypothesis should be the following: Gryffindor students have a higher GPA than Slytherin students.   

Explanation / Answer

A) She uses a huge spreadsheet with all of the GPAs of everybody in each house, and performs a two-sample z-test on this data to test for significantly different means in this case the error is Running Test on Entire Population

B) She takes a simple random sample of 70 individuals from each house. She calculates the mean GPA for each house and runs a two-sample z test on this data.in this case the error is Violation of Conditions for a test

C) She takes a simple random sample of 100 Gryffindor students and a simple random sample 25 Slytherin students. She performs a two-sample z-test on the data and concludes there is a difference in means in this case the error is Biased Sampling Method

D) She examines the sample data before performing the test, sees that the Gryffindors have higher GPAs than the Slytherins, and decides that the alternative hypothesis should be the following: Gryffindor students have a higher GPA than Slytherin students in this case the error is Incorrect Interpretation

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