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 [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 122 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 o.05 Ho: p = 0.20 Hai p# 0.20 Ho: p = 0.20 Ha: P 0.20 Ho: 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.) p-value = What can you conclude? Reject the null hypothesis. There is not sufficient evidence that more than 20% of the population of female workers is obese Do not reject the null hypothesis. There is sufficient evidence that more than 20% of the population of female workers is obese Do not reject the null hypothesis. There is not sufficient evidence that more than 20% of the population of female workers is obese (e) Reject the null hypothesis. There is sufficient evidence that more than 20% of the population of female workers is obese.

Explanation / Answer

The statistical software output for this problem is:

One sample proportion summary hypothesis test:
p : Proportion of successes
H0 : p = 0.2
HA : p > 0.2

Hypothesis test results:

Hence,

a) H0 : p = 0.2
HA : p > 0.2

z = 1.35

p - Value = 0.0890

Conclusion: Option C is correct.

Proportion Count Total Sample Prop. Std. Err. Z-Stat P-value p 122 547 0.22303473 0.017102765 1.3468427 0.089

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