Question

Each of 45 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. 33 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 (Use 2 decimal places)

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

Answer 1

Solution :

This is the rigt tailed test .

The null and alternative hypothesis is

H₀ : p = 0.5

H_a : p > 0.5

n = 45

x = 33

= x / n = 33 / 45 = 0.7333

P₀ = 0.5

1 - P₀ = 1 - 0.5 = 0.5

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.7333 - 0.5 / [(0.5 * 0.5) / 45]

= 3.13

Test statistic = 3.13

P(z > 3.13) = 1 - P(z < 3.13) = 1 - 0.9991 = 0.0009

P-value = 0.0009