5. Body mass index (BMI) is commonly used to estimate a healthy body weight based on how tall a person is. Suppose that we model the BMI measurements via normal distribution with mean µ=40 and standard deviation ?=5. Let $S^2$ denote the sample variance (a) If a random sample of 26 severely obese patients is observed i. what is the sampling distribution of $S^2$? ii. Find $P(S^2 < 16.5)$. (b) If a random sample of 20 severely obese patients is observed i. Find $P(S^2 > 12)$ ii. Find $g_1$ and $g_2$ so that $P(g_1 < S^2 < g_2) = .80$
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The sampling distribution of S^2 follows a chi-square distribution with (n-1) degrees of freedom, where n is the sample size. In this case, n = 26, so the sampling distribution of S^2 follows a chi-square distribution with 25 degrees of freedom. ii. Show more…
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A common characterization of obese individuals is that their body mass index is at least 30 [BMI = weight/(height)2, where height is in meters and weight is in kilograms]. An article reported that in a sample of female workers, 263 had BMIs of less than 25, 159 had BMIs that were at least 25 but less than 30, and 123 had BMIs exceeding 30. Is there compelling evidence for concluding that more than 20% of the individuals in the sampled population are obese? a. H0: p = 0.20 , Ha: p > 0.20 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z= p-value= b. What is the probability of not concluding that more than 20% of the population is obese when the actual percentage of obese individuals is 23%? (Round your answer to four decimal places.)
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A common characterization of obese individuals is that their body mass index is at least 30 [BMI = weight/(height)², where height is in meters and weight is in kilograms]. An article reported that in a sample of female workers, 266 had BMIs of less than 25, 158 had BMIs that were at least 25 but less than 30, and 123 had BMIs exceeding 30. Is there compelling evidence for concluding that more than 20% of the individuals in the sampled population are obese? (a) State the appropriate hypotheses with a significance level of 0.05. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = What is the probability of not concluding that more than 20% of the population is obese when the actual percentage of obese individuals is 25%? (Round your answer to four decimal places.)
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A common characterization of obese individuals is that their body mass index is at least 30 [BMI = weight/(height)², where height is in meters and weight is in kilograms]. An article reported that in a sample of female workers, 268 had BMIs of less than 25, 157 had BMIs that were at least 25 but less than 30, and 121 had BMIs exceeding 30. Is there compelling evidence for concluding that more than 20% of the individuals in the sampled population are obese? (a) State the appropriate hypotheses with a significance level of 0.05. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = ? P-value = ? (c) What is the probability of not concluding that more than 20% of the population is obese when the actual percentage of obese individuals is 25%? (Round your answer to four decimal places.)
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