A school psychologist was interested in whether the 12 students in the chess clu

Question

A school psychologist was interested in whether the 12 students in the chess club had a higher or lower mean grade point average (GPA) than the other students at a school. The overall GPA at the school is 2.55 with a standard deviation of 0.5. Use the .05 significance level to determine if the average chess club GPA is different from students in general at this school.

3.10     3.70     3.00     2.80     3.30     3.90

3.00     3.20     2.50     3.40     3.30     2.80

A) What is the appropriate test for this data?

B) Conduct the appropriate hypothesis test. Only hand calculate if you choose a z-test and then follow the five steps of hypothesis testing and provide a drawing. Otherwise, use SPSS.  

C) Give an interpretation of this data (one sentence conclusion of the hypothesis test that should be free of statistical jargon) and report the statistics in APA format.

D) Explain how you found the characteristics of the comparison distribution. In your explanation, be sure to use the names of the concepts. For example, if you are calculating variance for the distribution of means call it that. Do not simply say “that number”.

M = 3.17

SS = 1.69

SD = 0.37

Explanation / Answer

A) As population standard deviation is known we can use z-test to prove this hypthesis.

B) Below are the null and alternate hypothesis,
H0: mu <= 2.55
H1: mu > 2.55

Test statistics, z = (xbar - mu)/(sigma/sqrt(n))
z = (3.17 - 2.55)/(0.05/sqrt(12)) = 4.2954

p-value = P(z>4.3) = 0.000001

This p-value is less than the significance level of 0.05. Hence we reject the null hypothesis.

This means the mean GPA of 12 students is higher than the mean grade point average of the other students.

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