A common characterization of obese individuals is that their body mass index is at least 30 [BMI = weight/(height)", where height is in meters and weight is in kilograms]. An article reported that in a sample of female workers, 264 had BMIS of less than 25, 1 had BMIs that were least 25 but less than 30, and 122 had BMIS exceeding 30. Is there compelling evidence for concluding that more than 20% of the individuals in the sampled population are obese? USE SALT (a) State the appropriate hypotheses with a significance level 0.05. O Ho: P >0.20 H₂: P = 0.20 O Ho: P = 0.20 H: P = 0.20 O Ho: P = 0.20 H₂: p > 0.20 ⒸHO: P = 0.20 H: 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.) P-value= What can you conclude? O Do not reject the null hypothesis. There is not sufficient evidence that more than 20% of the population of female workers is obese. O Reject the null hypothesis. There is sufficient evidence that more than 20% of the population of female workers i s obese O Do not reject the null hypothesis. There is sufficient evidence that more than 20% of the population of female workers is obese. O Reject the null hypothesis. There is not sufficient evidence that more than 20% of the population of female workers is obese. (b) Explain in the context of this scenario what constitutes type I error. O A type I error would be declaring that 20% or less of the population of female workers is obese, when in fact more than 20% are actually obese. O A type I error would be declaring that 20% or more of the population of female workers is obese, when in fact less than 20% are actually obese. OA type I error would be declaring that less than 20% of the population of female workers is obese, when in fact 20% or more are actually obese. O A type I error would be declaring that more than 20% of the population of female workers is obese, when in fact 20% or less are actually obese. Explain in the context of this scenario what constitutes type II error. O A type II error would be declaring that 20% or less of the population of female workers is obese, when in fact more than 20% are actually obese. O A type II error would be declaring that 20% or more of the population of female workers is obese, when in fact less than 20% are actually obese. O A type II error would be declaring that less than 20% of the population of female workers is obese, when in fact 20% or more are actually obese. O A type II error would be declaring that more than 20% of the population of female workers is obese, when in fact 20% or less are actually obese. (c) What is the probability of not concluding that more than 20 % of the population obese when the actual percentage of obese individuals is 25% ? (Round your answer to four decimal places.)