A common characterization of obese Individuals is that their body mass Index is

Question

A common characterization of obese Individuals is that their body mass Index is at least 30 [BMIweight/(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 2S, 159 had BMIs that were at loost 2S but less than 30, and i21 had BMIs exceeding 30. is there compelling evidence for concluding that more than 20% of the individas n the sampled population are obese (a) State the appropriate hypothesps with a significance level of o.os ??, p . 0.20 Ha: P 0.20 O Ho: P0.20 Mai p = 0.20 Calculate the test statistic and determine the Pvalue. (Round your test statistik to two decimal places and your Pivalue to four decimal places.) P-value What can you conclude? O Do not reject the nul hypothesis. O Do not reject the nul hypothesis. There' O Reject the null hypothesis. su s. There is not sufficient evidence that more than 20% of the population of female workers is obese. sufficient evidence that is sufficient evidence that more than 20% of the population of fernale workers is obese. is. There is sufficient evidence that more than 20% of the population of female workers is obese. Reject the null hypothesis. There is not sumcent 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 ld be declaring that 20% or less of the population of female workers is obese, when in fact more than 20% are actually obese. A type t A type l error would be declar an 20% are actually obese. of female workers is obese, when in fact 20% or more are actually obese. le workers is obese, when in fact less th . ing that less than 20% of the population

Explanation / Answer

Ans:

a)Given that

n=544

sample proportion=121/544=0.2224

Test statistic

z=(0.2224-0.2)/sqrt(0.2*(1-0.2)/544)=1.31

p-value=P(z>1.308)=0.0955

(with rounding of z value to 1.31,p-value=0.0951)

As,p-value>0.05,we do not reject null hypothesis.There is not sufficient evidence that more than 20% of the population of female workers is obese.

(first option is correct.)

b)We make type I error,when we reject null hypothesis and null hypothesis is true.

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 obese.

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