A June 2009 Harris Interactive poll asked people their opinions about the influence of advertising on the products they buy. Among the people aged 18 to 34 years, 45% view advertisements as being influential, whereas among the people aged 35 to 44 years, 37% view advertisements as being influential. Suppose that this survey included 655 people in the 18- to 34-year age group and 420 in the 35- to 44- year age group. At the 1% significance level, can you conclude that the proportion of all people aged 18 to 34 years who view advertisements as being influential in their purchases is greater than the proportion of all people aged 35 to 44 years who hold the same opinion

We accept with 99 % of confidence that p₁ ( the proportion in the group aged 18 - 34 ) is bigger than p₂ (the proportion in the group aged 35-44)

Step-by-step explanation:

Group aged  18 - 34

Sample size n₁  =  655  sample size enough to apply a normal distribution aproximation for the test

p₁ = 0,45      and   q₁ =  1 - p₁      q₁ = 0,55

p₁*n₁  =  0,45*655 = 294     q₁*n₁  = 0,55*655 = 360

both bigger than 5

p₁  = 45 %     or     p₁  = 0,45          then  q₁  = 1 - 0,45    q₁ = 0,55

Group aged 35 - 44

Sample size  n₂  =  420 sample size enough to apply a normal distribution aproximation for the test

p₂  =  37%   p₂ = 0,37     and    q₂  = 0,63

p₂*n₂  =  0, 37*420 =  155     q₁*n₁  = 0,63*420 = 264

Test Hypothesis

Null Hypothesis        H₀                                             p₁  =  p₂

Alternative Hypothesis Hₐ                                        p₁  >  p₂

Significance level    α  =  1%   α  = 0,01

Confidence Interval     CI = 99 %

Then   from z table  we find   critical z   z (c )  = 3,1

Calculating   z(s)

z(s)  =  (  p₁ - p₂ )/ √[ ( p₁*q₁)/n₁ ] + [ (p₂*q₂)/n₂ ]

z(s ) = (0,45 - 0,37 ) /  √ 0,45*0,55)/655  +  0,37*0,63 /420

z(s)  = 0,08  /0,03

z(s) = 2,66

Comparing  z(s)  and z(c)

z(s) < z(c)

Then z (s) is inside the acceptance region for H₀

this is a direct variation proportion. y = kx

y is the total amount due, k is the constant of variation, and x is the number of texts sent.

plug in the 3.20 and the 16 to solve for the "k". this is the constant of proportionality. it is the value that will not change.

3.20 = k(16). solving you get $.20 per text.

the equation would then be y = .20x