Question

Each of 44 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...

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

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

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

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

Answer 1

a)

H0: p = 0.50 , Ha: p > 0.50

b)

Sample proportion $\hat{p}$ = 29/44 = 0.6591

Test statistics

z = $\hat{p}$ - p / sqrt( p( 1 - p) / n)

= 0.6591 - 0.50 / sqrt( 0.50 * 0.50 / 44)

= 2.11

This is test statistics value.

c)

p-value = P( Z > z)

= P( Z > 2.11)

= 0.0174

d)

Since p-value < 0.05 level, we have sufficient evidence to reject H0.

We conclude that

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