Question

Each of 53 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. 34 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)

Answer 1

a)

H0: p = 0.50 , Ha: p > 0.50

b)

Sample proportion = 34/53 = 0.6415

Test statistics

z = ( - p) / sqrt [ p (1 - p) / n ]

= ( 0.6415 - 0.50) / sqrt ( 0.50 * 0.50 / 53 )

= 2.06

c)

p-value = P(Z > z)

= P(Z > 2.06)

= 1 - P(Z < 2.06)

= 1 - 0.9803 (From Z table)

= 0.0197