To find a 95% confidence interval for the population proportion, we first need to calculate the sample proportion (p_hat). In this case, the sample proportion would be the proportion of organizations in the sample that responded positively to the survey, which is 810 out of 1200. Therefore, the sample proportion p_hat will be 810 / 1200.
Next, let's find out the standard deviation. The formula we will use is sqrt((p_hat * (1 - p_hat)) / N). This formula is used to calculate the standard error, a measure of the statistical accuracy of an estimate, equal to the standard deviation of the theoretical distribution of a large population of such estimates.
Now, we need to determine the z-score that corresponds to a 95% confidence interval. This corresponds to a point on the standard normal distribution, such that the area under the curve to the left of that point is 0.975 or (1 - (1 - 0.95)/2). In a standard Z-table, this z-score is roughly 1.96.
We then calculate the margin of error, according to the formula MoE = Z * standard error. In this case, it would be 1.96 times our calculated standard error.
Finally, to find the 95% confidence interval, we get the range of values by subtracting and adding the margin of error from/to the sample proportion.
By computing these values, we find that (0.6485, 0.7015) is our 95% confidence interval. This tells us that we can be 95% confident that the true population proportion of organizations that indicated "the need for collaboration among an increasing number of locations" as a business driver that led them to implement cloud solutions will fall between 64.85% and 70.15%.