Question

A new soft drink is being market-tested. A random sample of 100 consumers tasted the new drink and 65 liked it. Test to see if the company can claim that more than 60% of consumers like the drink. Use α = 0.05.

(a) Ho and Ha

(b) Test method, test statistic, and p-value

(c) Statistical decision and case-specific conclusion

Answer 1

a)

H0: p <= 0.6

Ha: p > 0.6

b)

We use z test.

Sample proportion = 65 / 100 = 0.65

Test statistics

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

= ( 0.65 - 0.60) / sqrt ( 0.60 ( 1 - 0.60) / 100 ]

= 1.02

p-value = P(Z > z)

= P(Z > 1.02)

= 0.1539

c)

Since p-value > 0.05 , Fail to reject H0.

We do not have sufficient evidence to conclude that more than 60% of consumers like the drink