For the basic subscribers, the sample proportion of churned subscribers is calculated as follows:
\[
\hat{p}_1 = \frac{868}{2750} \approx 0.3156
\]
For the premium subscribers, the sample proportion is:
\[
\hat{p}_2 = \frac{856}{2776} \approx 0.3084
\]
We will calculate the confidence interval for the difference in proportions \( \hat{p}_1 - \hat{p}_2 \) at a 95% confidence level. The formula for the confidence interval is given by:
\[
(\hat{p}_1 - \hat{p}_2) \pm z \sqrt{\frac{\hat{p}_1(1 - \hat{p}_1)}{n_1} + \frac{\hat{p}_2(1 - \hat{p}_2)}{n_2}}
\]
Where \( z \) is the critical value for a 95% confidence level, which is approximately \( 1.96 \).
Substituting the values:
\[
\hat{p}_1 - \hat{p}_2 = 0.3156 - 0.3084 = 0.0072
\]
Now, we calculate the standard error:
\[
\sqrt{\frac{0.3156(1 - 0.3156)}{2750} + \frac{0.3084(1 - 0.3084)}{2776}} \approx 0.0124
\]
Thus, the confidence interval becomes:
\[
0.0072 \pm 1.96 \cdot 0.0124
\]
Calculating the margin of error:
\[
1.96 \cdot 0.0124 \approx 0.0243
\]
Therefore, the confidence interval is:
\[
(0.0072 - 0.0243, 0.0072 + 0.0243) = (-0.0172, 0.0317)
\]
The confidence interval for the difference in proportions is:
\[
(-0.0172, 0.0317)
\]
Since this interval includes zero, we conclude that there is no significant difference in the proportion of churned subscribers between basic and premium plans.
There is no significant difference in the proportion of churned subscribers between basic and premium plans. The answer is:
\(\boxed{\text{There is no significant difference.}}\)