Question

Create and solve a population proportion for this parameter. Gather appropriate data and post your problem. Include the null and alternative hypothesis, alpha value, p-value, and a conclusion. Make sure that you use appropriate terminology, specify whether you are using the classical method or the p-value method, and fully explain your solution.

“A survey at a local school has revealed that 223 of its students own a smartphone, and that 90 of those 223 students own an iPhone.

Test this hypothesis at the .05 significance level

Answer 1

let the population proportion who owns an iphone=0.35 and school claims that this proportion is differnent from 0.35.

Ho :   p =    0.35
H1 :   p ╪   0.35

Level of Significance,   α =    0.05      
Number of Items of Interest,   x =   90      
Sample Size,   n =    223      
              
Sample Proportion ,    p̂ = x/n =    0.4036

   
              
Standard Error ,    SE = √( p(1-p)/n ) =    0.0319      
              
Z Test Statistic =    Z = ( p̂-p)/SE =    1.6777

              
p-value approach--   
p-Value   =   0.093   [excel formula =2*NORMSDIST(-z)]  

Conclusion:     p value>α ,do not reject null hypothesis

so, there is no enough evidence to conlcude that population proportion is different from 0.35 at α=0.05