Question

Each of 40 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. 29 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 H_a: p >  

(b) The test statistic is  (Use 2 decimal places)

(c) The p-value is  (Use 4 decimal places)

(d) Therefore, at the α = 0.05 level we can conclude that

The data provides statistical evidence that the majority of tasters prefer the fresh-brewed coffee.

The data does not provide statistical evidence that the majority of tasters prefer the fresh-brewed coffee.   

The data provides statistical evidence evidence that the majority of tasters do not prefer the fresh-brewed coffee.

The data does not provide statistical evidence that the majority of tasters do not prefer the fresh-brewed coffee.

Answer 1

The statistical software output for this problem is:

One sample proportion summary hypothesis test:
p : Proportion of successes
H₀ : p = 0.5
H_A : p > 0.5

Hypothesis test results:

Proportion	Count	Total	Sample Prop.	Std. Err.	Z-Stat	P-value
p	29	40	0.725	0.079056942	2.8460499	0.0022

Hence,

a) H0: p = 0.5 and Ha: p > 0.5

b) Test statistic = 2.85

c) p - Value = 0.0022

d) The data provides statistical evidence that the majority of tasters prefer the fresh-brewed coffee. Option A is correct.