Question

6. A common characteristic of obese individuals is BMI of at least 30. In a sample of workers at a factory, 262 have BMI less than 25, 159 have BMI at least 25 but less than 30, and 120 have BMI exceeding 30 a) Is there compelling evidence to conclude that more than 20% of the individuals in the sampled population are obese? Test at 5% significance level. Explain in this context the meanings of tyI und type II errors. What error you might have commited given your conclusion in part a)? b)

Answer 1

a)

Total number of workers : 262 + 159 + 120 = 541

Here we have n=541, p- 1-120, =0.2218 Hypotheses are Но: р-0.2 Ha:p>0.2 Level of significance : α-0.05 Test is right tailed The standard deviation is: sqrt((0.2*(1-0.2))/541) = 0.0172 Test Statistics: p-p F(0.2218-0.2)/(0.0172) = 1.27 Critical value: CV = 1.64 Rejection Region: If z > 1.64, Reject HO Decision: Since test statistics does not lie in rejection region so we fail to reject the null hypothesis P-value-0.102 P-value Decision: Since p-value is not less than level of significance so we fail to reject the null hypothesis Excel function for critical value: NORMSINV(1-0.05) Excel function for p-value: -1-NORMSDIST(1.27)

b)

Type I error: It is the probability of rejecting the true null hypothesis. That is researcher incorrectly conclude that more than 20% of the individuals are obese while actually it is less than equal to 20%.

Type II error: It is the probability of fail to reject the false null hypothesis. That is researcher incorrectly conclude that less than or equal to 20% of the individuals are obese while actually it is more than 20%.

Since we fail to reject the null hypothesis so type II error is possible.