. According to the National Center for Health Statistics, the mean weight for an adult female in the United States is 164.7 pounds. A group promoting healthier eating habits feels strongly that it has made an impact in one community by reducing the mean weight of women in that community. A simple random sample of 39 women in this community yielded a mean weight of 162.9 pounds. Assuming that the population standard deviation is 5.6 pounds, is the sufficient evidence at a a = 0.05 significance level to say that the mean weight of women in this community is lower than 164.7 pounds?

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