One of the questions in the Pew Internet & American Life Project asked adults if they used the Internet at least occasionally (Pew website, October 23, 2012). The results showed that 454 out of 478 adults aged 18 - 29 answered Yes; 741 out of 833 adults aged 30 – 49 answered Yes; 1058 out of 1644 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. 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.

Explanation:

S/N   Age range       Adult Population       Population Internet Users

A       18   -    29                 478                                 454

B       30   -    49                833                                 741

C       50 and above         1644                                1058

             Total                     2955                               2253

a) Let E = Estimate proportion and A = Internet users

Hence, n(E) = 478 and n(A) = 454

∴ Probability of Internet users (18 - 29), P(A) = n(A)/n(E) = 454/478 = 0.9498 (94.98%)

b) n(E) = 833 and n(B) = 741

∴ Probability of Internet users (30 - 49), P(B) = n(A)/n(E) = 741/833 = 0.8896 (88.96%)

c) n(E) = 1644 and n(C) = 1058

∴ Probability of Internet users (50 and above), P(C) = n(C)/n(E) = 1058/1644 = 0.6436 (64.36%)

d) Let Et = Total estimate proportion

Hence, n(Et) = 2955 and n(A) = 454

∴ Probability of 18 - 29 age range using Internet overall Pt(A) = n(A)/n(Et) = 454/2955 = 0.1536 (15.36%)

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