Final answer:
To estimate the standard error of sample proportions, calculate the sample proportions p' and q' from the dotplot, and then use the formula SE = √(p'*q'/n).
Step-by-step explanation:
To estimate the standard error of the sample proportions from a dotplot, we need the sample proportions, which can be calculated using the following steps:
- Identify the number of successes (x) in the sample from the dotplot.
- Calculate the estimated proportion of successes (p'), which is a point estimate for P, using the formula p' = x / n, where n is the total sample size.
- Find the estimated proportion of failures (q'), which is simply 1 - p'.
- Use the error bound formula to calculate the standard error (SE) for the proportion p', which is SE = √(p' * q' / n).
Remember that in the error bound formula, we use the sample proportions p' and q' as estimates because the actual population proportions p and q are unknown. Also, it's important to make sure that the sample size is large enough so that the Central Limit Theorem holds and the distribution of sample proportions is approximately normal, allowing us to use the above calculations reliably.
Lastly, to construct a 95 percent confidence interval for the true mean or proportion, use the point estimate (p') and the standard error to find the lower and upper bounds. You can include a sketch of the graph with the point estimate and the confidence interval marked.