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Answer:
To determine whether the people in that place are overweight or not, we need to calculate the sample mean and sample standard deviation of the body mass indices, and then conduct a hypothesis test with a significance level of 5%.
1. The sample mean of the body mass indices is:
x̄ = (24.2 + 33.1 + 24.2 + 29.9 + 30.4 + 32.8 + 17.5 + 23.1 + 28.7 + 24.2 + 27.8 + 29.4 + 19.6 + 28.5 + 28.2 + 25.7 + 22.0 + 29.0 + 35.9 + 18.5)/20 = 26.51
2. The sample standard deviation of the body mass indices is:
s = sqrt(Σ(xi - x̄)^2/(n-1)) = 5.621
3. Ho: The population mean body mass index is less than or equal to 24 kg/M2 (i.e., the people are not overweight).
4. Ha: The population mean body mass index is greater than 24 kg/M2 (i.e., the people are overweight).
5. The level of significance is α = 0.05.
6. Since the sample size is less than 30 and the population standard deviation is unknown, we will use the t-distribution.
7. The critical value of t for a one-tailed test with 19 degrees of freedom and a significance level of 0.05 is tc = 1.734.
8. The test statistic is:
t = (x̄ - 24)/(s/sqrt(n)) = 2.147
9. Decision Rule: Reject Ho if the test statistic t > tc.
10. The rejection region is t > 1.734.
11. Decision: Since t = 2.147 > 1.734, we reject Ho.
12. Conclusion: At a significance level of 5%, we have sufficient evidence to conclude that the population mean body mass index is greater than 24 kg/M2, which means that the people in that place are overweight.