A new sports drink is being tested in various markets. A sample of 400 people to

Question

A new sports drink is being tested in various markets. A sample of 400 people took part in a taste test and 80 replied that they liked the taste. What is the correct set of hypothesis if you want to test if at least? 22% of the population will like the new? drink? A. ?Ho: mugreater than or equals 0.22 ? Ha: mu ?< 0.22 B. ?Ho: muless than or equals 0.22 ? Ha: mu ?> 0.22 C. ?Ho: mu ?= 0.22 ? Ha: mu not equals0.22 D. ?Ho: munot equals 0.22 ? Ha: mu ?= 0.22 Using alpha ?= 0.05, what is the test statistic and what can you? conclude? A. ?Z= 0.22; reject Ho. B. ?Z= -1.645; do not reject Ho. C. ?Z= 1; accept Ha. D. ?Z= -1; do not reject Ho.

Explanation / Answer

Solution

Given that p = 80/400 = 0.20

(1) option (b)

?Ho: mu <= 0.22 ? Ha: mu ?> 0.22

(2) Z test statistic = (0.2-0.22)/((0.22)(1-0.22)/400)0.5 = -1

D. ?Z= -1; do not reject Ho.

(as Z critical value at 5% = -1.649)

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