Question

A Pew Research study finds that 23% of Americans use only a cell phone, and no land line, for making phone calls (The Wall Street Journal, October 14, 2010). A year later, a researcher samples 200 Americans and finds that 51 of them use only cell phones for making phone calls.Set up the hypotheses in order to determine whether the proportion of Americans who solely use cell phones to make phone calls differs from 23%.

Answer 1

Answer:

We accept H₀ sample does not give evidence to support that the proportion of Americans who solely use cell phone differs from 23 %

Step-by-step explanation:

A pew research finds  that  23 %  ( μ ) of Americans use only cell phone

Sample Information

sample size   n  = 200

x₁  =  51     then   p₁  = 51/200   p₁  =  0,255

and  q₁  =  1  - p ₁    q₁  =  1  - 0,255    q₁  =  0,745

Sample big enough for the approximation of the binomial distribution to the normal distribution

p₁*n  = 0,255 * 200 = 51  > 5   and   q₁*n    = 0,745* 200 =  149 > 5

Test hypothesis

Null hypothesis                       H₀              p₁  = μ = 0,23

Alternative hypothesis           Hₐ              p₁  ≠  0,23

Is a two tail test. We choose CI = 95 %  then significance level is                    α = 0,05 %

α = 0,05 as is a two tail test   α/2  = 0,025

from z-table  z(c) = 1,96

To calculate  z(s) = ( x  -  μ ) /√p₁*q₁/n  

  z(s) = ( 0,255 - 0,23 )/√0,255*0,745/200

z(s)  =  0,025 / 0,0308

z(s)  = 0,81

Comparing z(s)   and  z(c)

z(s) < z(c)      0,81 < 1,96

Then  z(s) is in the acceptance region: we accept H₀