Final answer:
To construct a 98% confidence interval for the difference of the mean amount of June precipitation in Michigan cities minus mean amount of June precipitation in Ohio cities, calculate the mean and standard deviation for both sets of data. The confidence interval is (-0.958, -0.082).
Step-by-step explanation:
To construct a 98% confidence interval for the difference of the mean amount of June precipitation in Michigan cities minus mean amount of June precipitation in Ohio cities, we need to find the mean and standard deviation for both sets of data.
Michigan mean = (3.46 + 3.27 + 3.62 + 2.68 + 2.68) / 5 = 3.34
Michigan standard deviation = sqrt((3.46 - 3.34)^2 + (3.27 - 3.34)^2 + (3.62 - 3.34)^2 + (2.68 - 3.34)^2 + (2.68 - 3.34)^2 / 4) ~= 0.413
Ohio mean = (3.15 + 4.17 + 4.06 + 3.86 + 4.17) / 5 = 3.86
Ohio standard deviation = sqrt((3.15 - 3.86)^2 + (4.17 - 3.86)^2 + (4.06 - 3.86)^2 + (3.86 - 3.86)^2 + (4.17 - 3.86)^2 / 4) ~= 0.503
Now, we can calculate the margin of error using the formula: margin of error = (Z)(standard deviation) / sqrt(sample size)
Z represents the z-score for the desired confidence level:
- For a 98% confidence level, the Z-score is approximately 2.33.
Using the formula, the margin of error is calculated as follows:
margin of error = (2.33)((0.413^2 / 5) + (0.503^2 / 5)) ~= 0.438
Finally, we can calculate the confidence interval using the formula: confidence interval = (mean difference) ± margin of error
confidence interval = (3.34 - 3.86) ± 0.438
confidence interval = -0.52 ± 0.438
confidence interval = (-0.958, -0.082)