Final answer:
To find the 95% confidence interval for the difference in proportions of large and small retailers using regression for forecasting, calculate the sample proportions for each group, the pooled sample proportion, the standard error, the Z-value for 95% confidence, the margin of error, and then establish the interval around the difference in sample proportions.
Step-by-step explanation:
The student is asking to determine a 95% confidence interval for the difference in proportions between two groups of retailers using regression for forecasting. To solve this, we'll need to calculate the standard error of the difference in proportions and then use a Z-score that corresponds to the 95% confidence level. We'll perform the following steps:
- Calculate each group's sample proportion: p1 = 90/125 for large retailers and p2 = 80/160 for small retailers.
- Calculate the pooled sample proportion: p = (90 + 80) / (125 + 160).
- Calculate the standard error of the difference: SE = sqrt(p * (1 - p) * (1/n1 + 1/n2)), where n1 is the sample size of the first group and n2 is the sample size of the second group.
- Find the Z-value that corresponds to a 95% confidence interval (typically 1.96).
- Calculate the margin of error: ME = Z * SE.
- Determine the confidence interval: (p1 - p2) ± ME.
After performing these calculations, we can find the interval that represents the difference in the proportion of large and small retailers using regression for forecasting with 95% confidence.