Question

In a survey conducted by a reputable marketing​ agency, 233 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).

​(a) What is the sample in this​ study? What is the population of​ interest?

Determine the sample in this study. Select the correct choice below​ and, if​ necessary, fill in the answer box within your choice.

A.

The sample is all adults 19 years of age or older.

B.

The sample is all adults.

C.

The sample is all adults with a cell phone.

D.The sample is the

nothing

adults 19 years of age or older.

​(Type a whole​ number.)

Determine the population of interest. Select the correct choice below​ and, if​ necessary, fill in the answer box within your choice.

A.

The population is all adults with a cell phone.

B.The population is the

nothing

adults 19 years of age or older.

​(Type a whole​ number.)

C.

The population is all adults 19 years of age or older.

D.

The population is all adults.

​(b) What is the variable of interest in this​ study? Is it qualitative or​ quantitative?

The variable of interest is

▼

the adults in the sample.

bringing one's cell phone every trip to the bathroom.

the age of the respondent.

This variable is

▼

qualitative with two outcomes

quantitative

because

▼

numerical measures of individuals are provided.

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.

ModifyingAbove p with caretpequals=nothing

​(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.

It is being used to make inferences.

B.

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

C.

It is information obtained from a survey.

D.

Its value is based on a sample.

E.

The sample size is large.

Why is the point estimate found in part​ (c) a random​ variable?

A.

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

B.

It is information obtained from a survey.

C.

The sample size is large.

D.

It is being used to make inferences.

E.

Its value is based on a sample.

What is the source of variability in the random​ variable?

A.

The sample size

B.

Random errors

C.

The individuals selected to be in the study

D.

The question asked in the survey

​(e) Construct and interpret a

9595​%

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.)

A.There is a

nothing​%

probability the proportion of adults 19 years of age or older who bring their cell phone every trip to the bathroom is between

nothing

and

nothing.

B.We are

nothing​%

confident the proportion of adults 19 years of age or older who bring their cell phone every trip to the bathroom is between

nothing

and

nothing.

​(f) What ensures that the results of this study are representative of all adults 19 years of age or​ older?

A.

The high confidence level

B.

Random sampling

C.

The large sample size

D.

Sampling from adults 19 years of age or older

Answer 1

(a) Sample:

Answer: D.The sample is the 1000 adults 19 years of age or older.

Population of interest:

Answer: C. The population is all adults 19 years of age or older.

​(b) The variable of interest is bringing one's cell phone every trip to the bathroom.

This variable is qualitative with two outcomes because individuals are classified based on a characteristic.

​(c)

p̂ = x/n = 0.233

​(d) Answer: D. Its value is based on a sample.

--

Why is the point estimate found in part​ (c) a random​ variable?

Answer: A. Its value may change depending on the individuals in the survey.

--

What is the source of variability in the random​ variable?

Answer: C. The individuals selected to be in the study

​(e)

95% Confidence interval :  

At α = 0.05, two tailed critical value, z_c = NORM.S.INV(0.05/2) =    1.960

Lower Bound = p̄ - z_c*√( p̄ *(1- p̄ )/n) = 0.233 - 1.96 *√(0.233*0.767/1000) =    0.207

Upper Bound = p̄ + z_c*√( p̄ *(1- p̄ )/n) = 0.233 + 1.96 *√(0.233*0.767/1000) =    0.259

Answer B.We are 95​% confident the proportion of adults 19 years of age or older who bring their cell phone every trip to the bathroom is between 0.207 and 0.259.

​(f) Answer: B. Random sampling