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.
H0: p >= 0.40
Ha: p < 0.40
Sample proportion = 70 / 200 = 0.35
z = ( - p) / sqrt [ p( 1 - p) / n ]
= ( 0.35 - 0.40) / sqrt ( 0.40 * ( 1 - 0.40) / 200 )
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.
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