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Correlation Test, Regression, Confidence Interval, Significant Difference

1. Two groups of 15 plants were grown under the same controlled conditions, but each group was treated with a different fertilizer. The results for the differences in plant size are: Ed =314, Ed^2=26513.38. At a 2% significance level, is there a significant difference between the fertilizers?

2. A sample of 94 students at a community college was taken to determine information about commuting distances to school. Sixty-four students reported commuting distances of more than 5 miles. Determine the 95% confidence interval for the proportion of students,p, who commute more than 5 miles?

3. The director of human resources in a corporation believes that the distribution of education levels among new employees is the same as among new hires two years ago. The distributions are as follows:

Distribution two years ago

Education level/Percent
High School -25.7%
College 2 years - 29.5%
College 4 years - 37.0%
Graduate - 7.8%

Distribution this year

Education level/Observed
High School - 18
College 2 years - 49
College 4 years - 48
Graduate - 13

Test the hypothesis at a 10% significance level.

4. Given the following statistics:
Ex=270, Ey=3023, Exy=94,123, Ex2= 8316, n=9, SST=79,444.9, SSR=54,562.4,
SSE= 24,882.5

a. Find the regression equation
b. Compute the coefficient of determination
c. Compute the correlation coefficient
d. Comment on the usefulness of the regression to make predictions

5. Perform the correlation test:
H0: p=0
Ha: p not equal to 0
at the 5% significance level, given n=11 and r= -0.331

Solution Summary

5 hypothesis testing questions covering these topics are worked out and explained in an attached .doc file.