Question

McDonald’s is offering a new product. You want to test to see whether more than sixty percent of customers will purchase the product. 200 customers are surveyed, and 125 say they will buy it.
(a) Write down an appropriate null and alternative hypothesis. (b) Construct the test statistic. (c) Test your hypothesis at all levels.

Answer 1

a)

Ho :   p =    0.6  
H1 :   p >   0.6   (Right tail test)

b)

Number of Items of Interest,   x =   125
Sample Size,   n =    200
      
Sample Proportion ,    p̂ = x/n =    0.6250
      
Standard Error ,    SE = √( p(1-p)/n ) =    0.0346
Z Test Statistic = ( p̂-p)/SE =    (0.625-0.6)/0.0346=   0.72

c)

p-Value   =   0.2352   [Excel function =NORMSDIST(-z)
Decision:   p value>α ,do not reject null hypothesis       

Null hypothesis is not rejected at α=0.001,0.01,0.05,0.10