Question

In a survey conducted by a reputable marketing agency, 252 of 1000 adults 19 years of age or older confessed to bringing and using their cell phone every trip to the bathroom (confessions included texting and answering phone calls). Complete parts (a) through (f) below. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). Why is the point estimate found in part (c) a random variable? O A. It is being used to make inferences. OB. Its value is based on a sample. OC. It is information obtained from a survey. D. Its value may change depending on the individuals in the survey. O E. The sample size is large. What is the source of variability in the random variable? O A. The question asked in the survey B. Random errors The individuals selected to be in the study OD. The sample size (e) Construct and interpret a 95% confidence interval for the population proportion of adults 19 years of age or older who bring their cell phone every trip to the bathroom. Select the correct choice below and fill in any answer boxes within your choice. (Type integers or decimals rounded to three decimal places as needed. Use ascending order.) O A. There is a % probability the proportion of adults 19 years of age or older who bring their cell phone every trip to the bathroom is between and OB. We are % confident the proportion of adults 19 years of age or older who bring their cell phone every trip to the bathroom is between and

Answer 1

1. D. Its value may change depending on the individuals in the survey.

2. A. There is a % probability the proportion of adults 19 years of age or older who bring their cell phone every trip to the bathroom is between and.

Step-by-step explanation:

In the given context, the point estimate found in part (c) is a random variable because it depends on the individuals in the survey. The value of the point estimate may change from one sample to another, reflecting the variability in responses among different sets of individuals.

Therefore, option D, "Its value may change depending on the individuals in the survey," is the correct choice.

Now, moving on to constructing and interpreting a 95% confidence interval for the population proportion of adults bringing their cell phones to the bathroom.

This interval is calculated based on the sample proportion, and the variability in this estimate is influenced by the individuals surveyed. The confidence interval represents a range within which we are reasonably confident the true population proportion lies.

Option A, "There is a % probability the proportion is between and," correctly captures the essence of a confidence interval, indicating the probability or confidence level associated with the estimated range.

This reflects the uncertainty inherent in estimating population parameters from a sample and provides a measure of the precision of the estimate.

Answer 2

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.