Given the three possible causes of a spike in favorable ratings (restaurant campaign, actual customer sentiment, and random variation) and discuss the role of a hypothesis test in distinguishing among the three causes.

A social media site that allows community members to rate restaurants wants to ensure that the reviews are genuine reviews of the community and not favorable reviews orchestrated by the friends of the restaurant owners. It uses several metrics when examining reviews, one of which is the “percent favorable.” It theorizes that a spike in the percent favorable might represent a campaign by the restaurant, but also recognizes that it might reflect genuine customer sentiment, or just random variation. So it collects 4 days’ worth of such data on a periodic basis and subjects it to a hypothesis test. For one restaurant, the percent favorable has stood at 60% for the last year. One recent 4-day sample showed 72% favorable—23 favorable reviews and 9 unfavorable.

(a) Specify and conduct an appropriate hypothesis test.

(b) In a couple of sentences, interpret the results of your hypothesis test.

(c) Given the three possible causes of a spike in favorable ratings (restaurant campaign, actual customer sentiment, and random variation) and discuss the role of a hypothesis test in distinguishing among the three causes.

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