Percentages of public school students in fourth grade in 1996 and in eight grade

Question

Percentages of public school students in fourth grade in 1996 and in eight grade in 2000 who were at or above the proficient level in mathematics were found as listed. Your task is to summarize the relationship between 1996 fourth-grade math proficiency percentage (x) and 2000 eight-grade math proficiency percentage (y). Examine these data and write a report. In your report, you should: Include appropriate graphs and statistics; Describe the association between 4th grade math scores and 8th grade math scores; Create the appropriateness of your model; Interpret the lope and y-intercept of the line in context; Use your model to interpret and discuss the reasonableness of a predicted 2000 eight-grade math proficiency for Nevada if the 1996 fourth-grade math proficiency was 14%? How does this prediction compare to the actual eighth-grade value of 20 for Nevada?

Explanation / Answer

a) Scatter plot

b) from above plot we conclude that there is a positive relation between x and y

c) The regression model is

y=a+bx

from excel

From the above analysis

y=-3.14 + 1.522(x)

d)

H0: Model is not significant

H1: Model is significant

alpha:5%

Test statistic:

from Excel

From above analysis

F=12.52

Conclusion:

P value=0.012 <0.05 we reject the H0. Hence claim is significant

Coefficients Standard Error t Stat P-value Intercept -3.13603 7.732456302 -0.40557 0.699127 X 1.522059 0.430078971 3.539022 0.012233

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