Question

One of the questions on a survey asked adults if they used the internet at least occasionally. The results showed that 457 out of 478 adults aged 18–29 answered Yes; 743 out of 833 adults aged 30–49 answered Yes; 1,061 out of 1,644 adults aged 50 and over answered Yes. (Round your answers to four decimal places.)

(a)

Develop a point estimate of the proportion of adults aged 18–29 who use the internet.

(b)

Develop a point estimate of the proportion of adults aged 30–49 who use the internet.

(c)

Develop a point estimate of the proportion of adults aged 50 and over who use the internet.

(d)

Comment on any relationship between age and Internet use that seems apparent. (multiple Choice)

-Adults aged 30–49 are less likely to use the internet than adults aged 50 and over.

-Older adults are more likely to use the internet.    

-Younger adults are more likely to use the internet.

-Adults aged 30–49 are the least likely to use the internet.

(e)

Suppose your target population of interest is that of all adults (18 years of age and over). Develop an estimate of the proportion of that population who use the internet.

Answer 1

The point estimate of proportion is given by maximum liklihhod estimation .

if X~Binomial(n,p)

liklihhod function L(x,p)=

taking log

log L = log(constant)+x*logp+(n-x)*log(1-p)

taking derivative with respect to p and putting it to 0 and solving for p

x*(1-p)-(n-x)*p=0

x -x*p-np+x*p=0

this means the point estimate of proportion is sample proportion

a) let x = number of people betwwen age (18-29) who used internet at least occasionally .

and p be there respective probabilities

point estimate of the proportion of adults aged 18–29 who use the internet is

  

= 0.9561

b) let x = number of people betwwen age (30-49) who used internet at least occasionally .

and p be there respective probabilities

=0.892

c) let x = number of people age 50 and above who used internet at least occasionally .

and p be there respective probabilities

=0.6454

d) 3rd statement --Younger adults are more likely to use the internet.

    This statement is pretty obvious as the young generation use more internet .This is evidently proven by the statistics as the proportion of the people who says yes for using the internet at least occasionally decrease as the age increases. Young generation uses the internet more for entertainment and work as well the young generation is more familiar with new technology than the older young generation, so this statement is apparent