Question 8: The current advertising campaign for a major soft drink brand would be changed if less than 30 percent of consumers like it. a) Formulate the null and alternative hypothesis b) Discuss the Type land Type II errors that could occur in hypothesis testing. c) Which statistical test would you use? Why? d) A random sample of 300 consumers was surveyed, and 84 respondents indicated that they liked the campaign. Should the campaign be changed? Why?

EXPERT ANSWER

a)

Ho : p = 0.3
H1 : p < 0.3

b)

Type I error is concluding that less than 30% of custimers like it while in actual it equal or greater than 30%

Type I error is concluding that equal to or greater than 30% of custimers like it while in actual it less than 30%

or

type I error is when current ad compaign is changed when it should not be changed

Type II error is when current ad compaign is not changed when it should be changed

c) Z test for one proportion

d)

Ho : p = 0.3
H1 : p < 0.3 (Left tail test)

Level of Significance, α = 0.05
Number of Items of Interest, x = 84
Sample Size, n = 300

Sample Proportion , p̂ = x/n = 0.2800

Standard Error , SE = √( p(1-p)/n ) = 0.02646
Z Test Statistic = ( p̂-p)/SE = (0.28-0.3)/0.0265= -0.7559

critical z value = -1.645 [excel function =NORMSINV(α)]

p-Value = 0.2248 [excel function =NORMSDIST(z)]
Decision: p value>α ,do not reject null hypothesis
There is not enough evidence that to conclude that current ad compaign should be changed