Question

A research center claims that at most 18% of U.S. adults’ online food purchases are for snacks. In a random sample of 1995 U.S. adults, 20% say their online food purchases are for snacks. At ? = 0.05, is there enough evidence to support the center’s claim?

a.) Identify ?0∶ _______________ and ??: ____________

b.) Find the standardized test statistic, z. ? = ?̂ ̅−? √??/?

c.) For = 0.05, find and describe the rejection region. Identify and label the appropriate z-score.

d.) Determine whether to reject or fail to reject ?0 .

e.) Interpret this decision in the context of the original claim.

Answer 1

a)

H0: p 0.18

Ha: p > 0.18

b)

Test statistics

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

= (0.20 - 0.18) / sqrt [ 0.18 ( 1 - 0.18) / 1995 ]

= 2.33

c)

Critical value at 0.05 level = 1.645 (From Z table)

d)

Since z-score falls in rejection region, Reject H0.

e)

We have sufficient evidence to conclude that at most 18% of U.S. adults’ online food purchases are for snacks.