5. Testing for differences in student height.a) The average height of 6th grade

5. Testing for differences in student height.a) The average height of 6th grade girls in the Kansas is 61.8 inches and the average height of 6th grade boys in Kansas is 59.4 inches. Are the heights of the boys and girls at Oceanview statistically different from the statewide averages?b) Is there a statistically significant difference between male and female height among sixth graders at this school?6. Teacher Qualitya) Calculate and compare the means of student test scores by class.b) Test to see if the differences in test scores are statistically significant. Which teachers have better performing students than others? Which have worse performing students?c) Can this be used as conclusive evidence that some of the teachers are better/worse at teaching than others?d) Repeat steps a and b using IQ scores instead of test scores. Does this change your response to part c?e) The statewide average on the standardized test is 75. First assume that you do not know the standard deviation for the population. How well does the school perform relative to the state average? How well does each teacher perform relative to the state average?
f) Repeat step e this time using the fact that the statewide standard deviation of test scores is 8.g) In parts e and f what are the null and alternate hypotheses? Given those hypotheses what would constitute a type I or a type II error? Did discovering the true population standard deviation in part f reveal any type I or type II errors in part e?7. Intelligence and Test scoresa) Construct a scatter plot of IQ and test scoresb) Estimate the relationship between IQ and test scores using regression analysisc) Interpret the Y intercept and beta coefficient. Are the results significant?d) IQ is surely not the only determinant of student test scores. Estimate the relationship between class attendance measured as days missing from class and test scores.e) Interpret the Y intercept and beta coefficient. Are the results significant?f) Estimate test scores using BOTH IQ and attendance as independent variables. How do these relate to your answers to b-e?g) What other variables (i.e. ones not in the dataset) do you think might be correlated with test scores? Why?