Question

In a survey conducted by the marketing agency 11mark, 241 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).
(a) What is the sample in this study? What is the population of interest?
(b) What is the variable of interest in this study? ls it qualitative or quantitative?
(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.
(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?
(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.
(f) What ensures that the results of this study are representative of all adults 19 years of age or older?

Answer 1

Answer: kindly check explanation

Step-by-step explanation:

A) The sample is a fraction of the total population used in the study.

The sample is 1000 19 years of age or older U.S adult.

The population : all U.S adults aged 19 or older.

B.) Confession about bringing cell phone to the bathroom and it is a qualitative variable

C.) point estimate (p) :

Total number of sample = 1000

Number who confessed to bring cellphone = 241

p = 241/ 1000

= 241/1000 = 0.241

D.) The point estimate was deduced from the sample information and not the population. Random selection because selection is unbiased.

E.) 95% confidence interval (CI)

95% CI = (1 - 0.95) = 0.05

For a two-tailed test : 0.05 / 2 = 0.025

Z - score = 1.96

Error : (√[p(1 - p) / n])*z

1.96 * √0.241(1-0.241)/1000

1.96* √0.000182919

1.96 * 0.0135247

= 0.0265085

Boundary :

(0.241 - 0.0265085), (0.241 + 0.0265085)

(0.2144915, 0.2675085)

F) The sample can be said to be representative of the total population since the sampling was performed and participants were chosen at random.