Question

2. A shopping center developer claims in a presentation to a client that at least 40% of the adult female population in a community visit the mall one or more times in a week. To evaluate this claim, a research firm selects a random sample of 200 adult females from the community and finds that 70 of the 200 say that they visit the mall one or more times in a week. Does this data provide enough evidence to disprove the developer’s claim? Use a significance level of .05.   

Answer 1

H0: p >= 0.40

Ha: p < 0.40

Sample proportion = 70 / 200 = 0.35

Test statistics

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

= ( 0.35 - 0.40) / sqrt ( 0.40 * ( 1 - 0.40) / 200 )

= -1.44

z critical value at 0.05 significance level = -1.645

Since test statistics > -1.645, do not reject H0.

We conclude at 0.05 significance level that, we do not have sufficient evidence to disprove

the developers claim.