Interpretation Types of Hypothesis Discussion

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Vgjnef01

Mathematics

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1. This semester, you have learned how to conduct and interpret several types of hypothesis tests. They are listed here: non-directional z-score hypothesis test (Chapter 8) directional z-score hypothesis test (Chapter 8) non-directional one sample t-test (Chapter 9) directional one sample t-test (Chapter 9) non-directional independent-measures t-test (Chapter 10) directional independent-measures t-test (Chapter 10) non-directional repeated-measures t-test (Chapter 11) directional repeated-measures t-test (Chapter 11) one-way independent-measures ANOVA (Chapter 12) one-way repeated-measures ANOVA (Chapter 13) two-factor independent-measures ANOVA (Chapter 13) non-directional correlation hypothesis test (Chapter 14) directional correlation hypothesis test (Chapter 14) chi-square goodness-of-fit test (Chapter 15) chi-square independence test (Chapter 15) Below you will find 5 scenarios. For each scenario, please pick which of the techniques listed above is the appropriate one to use to analyze the data and give a sentence explanation as to why you chose the technique you chose. NOTE: You do not actually have to calculate anything or conduct the hypothesis test. You can write your answers directly in your submission or you can attach a word/pdf file with your answers. Each question will be graded out of 2 points, for a total of 10 possible BONUS points. The BONUS points will be worth up to 5% extra on your overall grade. For example, if you get 10/10 on this BONUS Assignment, you will have 5% added to your final grade. If you get 8/10, you will have 4% added, and so on. Scenario 1: Brian is a math teacher who is interested in comparing three of his calculus classes - a basic level class, an honors level class and an AP level class. He gives students in all three classes the same test and then compares their scores. Brad wants to determine if there are any significant differences among the grades in the three classes. Scenario 2: It is well known that the average IQ in the general population is 100, with standard deviation 15. Jeremy's class has an average IQ of 110 and Jeremy wants to know whether his class has a significantly higher average IQ than the average in the general population. Scenario 3: Brad knows that 20% of people in the general population believe in astrology. He asks a group of 100 people whether or not they believe in astrology and wants to determine if his sample departs significantly from the general population. Scenario 4: Sarah wants to know if there is a significant relationship between whether or not a student attended a review class and whether or not a student passed the final exam. For each variable, Sarah notes a yes or no answer for each student. Scenario 5: Olivia believes that proximity significantly affects how often she sees her friends. To test this, Olivia notes how many times (in a year) she sees a sample of 5 friends who all live in the same city as Olivia. Then, Olivia spends a year studying abroad and notes how many times she again sees this same sample of 5 friends, now that they are all living in a different country. Olivia compares the two sets of sample scores to determine if there is a significant difference in how often she sees her friends when living in the same city vs. abroad.
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Hypothesis Tests

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Hypothesis Tests
Scenario 1:
Brian is a math teacher who is interested in comparing three of his calculus classes - a basic level
class, an honors level class and an AP level class. He gives students in all three classes the same
test and then compares their scores. Brad wants to determine if there are any significant
differences among the grades in the three classes.
Answer: the one-way repeated measures ANOVA
It is a statistical test used to determine if three or more related groups have a significant
difference amongst themselves due to a variable of interest. Here the variable of interest should be
normally distributed, continuous, and spread across the groups. E.g., In Scenario 1, we have a basic
level class, an honors-level class, and an AP level class hence having three groups. Also, the
variable of interest, which is the calculus classes, is common to all three groups, thereby making
the hypothesis test much appropriate.
Scenario 2:
It is well known that the average IQ in the general population is 100, with standard deviation
15. Jeremy’s class has an average IQ of 110 and Jeremy...

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