A study showed that 69 of supermarket shoppers believe super

A study showed that 69% of supermarket shoppers believe supermarket brands to be as good as national name brands. To investigate whether this result applies to its own product, the manufacturer of a national name-brand ketchup asked a sample of shoppers whether they believed that supermarket ketchup was as good as the national brand ketchup. If a sample of 100 shoppers showed 57 stating that the supermarket brand was as good as the national brand, what is the p-value (to 4 decimals)?

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.69
Ha:   p   =/=   0.69
As we see, the hypothesized po =   0.69      

Getting the point estimate of p, p^,          
          
p^ = x / n =    0.57      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.046249324      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -2.5946325      
          
As this is a    2   tailed test, then, getting the p value,  
          
p =    0.009469211 = 0.0095   [ANSWER]