People who experience online harassment either ignore it or respond via postings or involving authorities Is one method more effective than the other? A 2014 Pew Research Center report, based on a random sample of American adults, found that 412 of the 549 respondents who had chosen to ignore online harassment thought that it was an effective way to deal with the issue. Of the 368 respondents who had chosen to respond to online harassment, 305 thought that it had been effective A. Required:
a. Is there good evidence that one approach is more likely to be effective than the other? State the null and alternative hypotheses, obtain the test statistic and P-value, and conclude in context.
b. How large is the difference? Obtain and interpret in context a 95% confidence interval for the difference between the proportions of American adults who find ignoring online harassment effective and those who find responding to it effective.
c. How effective is that best method? Obtain and interpret in context a 95% confidence interval for theproportion of American adults who find the best m ethod effective.

Step-by-step explanation:

First method information:

Sample size  n₁  = 549

x₁ ( people ignoring on-line harassment )  =  412

Proportion of people ignoring on-line harassment  p₁

p₁ =  412/549   p₁  =  0,75   q₁ =  1  -  p₁    q₁ = 0,25

Second method ( people chosen to respond)

Sample size   n₂  =  368

number of people responding   x₂  = 305

Proportion of people responding

p₂ =  305/ 368    p₂ =  0,83   then  q₂  =  0,17

a) Looking for differences in the approachs

Hypothesis test:

Null Hypothesis                     H₀         p₁  =  p₂

Alternative Hypothesis         Hₐ         p₁  ≠  p₂

Alternative Hypothesis indicates that the test is a two-tail test

Choosing a confidence interval  CI = 95 % then a significance level is       α = 5%     α  = 0,05  and from z-table we get  z(c) =  1.64

To calculate z(s)

z(s)  =  (  p₁  -  p₂ ) / EED

EED = √  p₁*q₁)/n₁  +  (p₂*q₂)n₂

EED = √  (0,75*0,25)/549   +  0,83*0,17)/368

EED = √ 3,41 *10⁻⁴   +  3,83*10⁻⁴

EED =   10⁻² *√ 3,41 + 3,83

EED =   10⁻² * 2,69

EED = 0,0269

z(s)  =  (  p₁  -  p₂ )/0,0269

z(s)  = -  0,08 / 0,0269

z(s)  =  - 2,97

p-value for z(s)  is  pvalue  = 0,0015

Comparing  z(s)  and  z(c)   modules

z(s) > z(c)  therefor z(s) is in the rejection region we have to reject H₀ and claim that there is a difference between the proportions

b) How large is the difference