Each of 58 subjects tastes two unmarked cups of coffee and s

Each of 58 subjects tastes two unmarked cups of coffee and says which he or she prefers. One cup in each pair contains instant coffee, the other fresh-brewed coffee. 30 of the subjects prefer the fresh-brewed coffee. Take p to be the proportion of the population who would prefer fresh-brewed coffee in a blind tasting. Test the claim that a majority of people prefer the taste of fresh-brewed coffee.

(a) H0: p =
and Ha: p >
(b) The test statistic is

(c) The p-value is

Solution

a)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.5
Ha:   p   >   0.5 [ANSWER]

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b)

As we see, the hypothesized po =   0.5      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.517241379      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.065653216      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    0.262612866   [ANSWER]

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c)  
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.396424491   [ANSWER]

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