Question

in a survey conducted by a reputable marketing agency, 245 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
the variable of interest is bringing ones cell phone every trip to the bathroom. this variable is qualitative with two outcomes because individuals are classified based on a characteristic
(c) based on the results of this survey, obtain a point estimate for the proportion of adults 19 years of age or older who bring their cell phone every trip to the bathroom.
\\( \hat { p } = 0.245 \\)
(round to three decimal places as needed.)
(d) explain why the point estimate found in part (c) is a statistic. explain why it is a random variable. what is the source of variability in the random variable?
why is the point estimate found in part (c) a statistic?
a. the sample size is large.
b. its value may change depending on the individuals in the survey.
c. all pieces of information obtained from surveys are statistics.
d. its value is based on a specific sample.
e. it is being used to make inferences

Explanation:

A statistic is a numerical summary of a sample. In this case, the point estimate \(\hat{p}=\frac{245}{1000} = 0.245\) is calculated from a sample of 1000 adults. A random variable is a variable whose value is determined by the outcome of a random event. Here, the sample (and thus the value of \(\hat{p}\)) is randomly selected from the population of all adults 19 years of age or older. The source of variability is the fact that different samples of the same size from the population will yield different values of \(\hat{p}\) due to sampling variability.

Answer:

D. Its value is based on a specific sample.