Social scientists have designed a “happiness survey” that attempts to measures how happy people feel in their lives, on a scale of 1–100 (100 is the happiest). Extensive testing across the country shows that the mean score of U.S. citizens is 63 with a standard deviation of 23.2. The mayor of Eugene claims that people who live in this city have happier lives than average. We give the happiness survey to an SRS of 50 people and find an average score of 67. To what extent does this provide evidence for the mayor’s claim?
Social scientists have designed a “happiness survey” that attempts to measures how happy people feel in their lives, on a scale of 1–100 (100 is the happiest). Extensive testing across the country shows that the mean score of U.S. citizens is 63 with a standard deviation of 23.2.
The mayor of Eugene claims that people who live in this city have happier lives than average. We give the happiness survey to an SRS of 50 people and find an average score of 67. To what extent does this provide evidence for the mayor’s claim?
Let ?μ denote the average happiness score for people in Eugene.
If we assume that ?=63μ=63, what would be the probability of getting an average score of at least 67 from a SRS of 50 people? We would compute this via which
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