Final answer:
The point estimate in part (c) is a random variable because its value is based on a sample and is subject to random sampling variability. To calculate the 95% confidence interval for the population proportion of adults who bring their cell phone to the bathroom, use the sample proportion as the point estimate, calculate the standard error and margin of error, and apply the formula for confidence interval construction.
Step-by-step explanation:
In part (c) of the given schoolwork question, the point estimate is considered a random variable because its value is based on a sample (random sampling variability).
That is, every time we take a new sample, we expect different people to be included in it, which may lead to different survey results.
Thus, the source of variability in the random variable is the individuals selected to be in the study (selection of the individuals).
To estimate the population proportion of adults who bring their cell phone every trip to the bathroom with 95% confidence,
We use the sample proportion (p) as the point estimate for the population proportion, which is the number of adults who admitted to bringing their cell phone to the bathroom (252) divided by the total number of adults surveyed (1000).
Then we calculate the standard error (SE) using the formula SE = sqrt(p(1-p)/n), and find the margin of error (E) using the z-score corresponding to the desired confidence level, which is typically 1.96 for 95% confidence.
The confidence interval is then p ± E.
Therefore, to construct and interpret the 95% confidence interval, we first calculate the sample proportion p = 252/1000 = 0.252.
The standard error SE is then given by SE = sqrt(0.252(1-0.252)/1000). We use the z-score for 95% confidence, which is 1.96, to calculate the margin of error E = 1.96 × SE.
Finally, we construct the 95% confidence interval by subtracting and adding the margin of error from the sample proportion, which gives us a range that we are 95% confident contains the true population proportion of adults.