Flop e People Window Help secure Do Homework Kimberly Pacheco Math 112:TTh 41025

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Flop e People Window Help secure Do Homework Kimberly Pacheco Math 112:TTh 41025g6138questionld 18flushed false&old; 4326093&oentenw; 1-3 Tue Homework: Section 7.3 Homework Score: 0.5 of 1 pt 7 of 10 (3 complete) v 7.3.41 HW score: 20%, 2 of 10 pts A recent study Question Help from this reported that 56% of the children in a particular community were overweight or obese. Suppose a random sample of 400 public school chldren is taken community. Assume the sample was taken in such a way that the conditions for using the Central Limit Theorem are met. We are interested in finding the probability that the proportion of children in the sample wil be 0.53 parts and a. Before doing any calculations, determine whether this probability is greaterthan 50% or lessthan 50%. why? o A. The answer should be greater than 50%, because the resulting z-score will be positive and the samplng di is approximately Normal. B. The answer should be greater than 50%, because o.53 is less than the population proportion of 0.56 and because the sampling distribution is approximately Normal O c. The answer should be less than 50%, because the resultingzscore will be negative and the sampling distributionisapproximately Normal. O D. The answer should be less than 50%, because o 53 is less than the population proportion of 0.56 and because the samplng distrbution is approximately Normal. b. Calculate the probability that 53% or more of the sample are overweight or obese. P(p 2053) (Round to three decimal places as needed.) Enter your answer in the answer box and then click Check Answer. Clear All All parts showing To see what to study next, go to your Study Plan

Explanation / Answer

Q. 7.3.41

a. The answer should be greater than 50%, because 0.53 is less than the population proportion of 0.56 and because the sampling distribution is approximately normal.

Here resulting z - score is negative so option A is incorrect.

b. p( p^ >= 0.53) = ?

Mean p^ = 0.56 and std. dev. = sqrt (p*(1-p) /n) = sqrt [ 0.56 * 0.44/400] = 0.0248

so Z - value = ( 0.53 - 0.56)/ 0.0248 = - 1.21

Relative p - value = 0.1131

so p( p^ >= 0.53) = 1- 0.1131 = 0.8869

Q. 7.3.42

a. The answer should be greater than 50%, because 0.30is more than the population proportion of 0.26 and because the sampling distribution is approximately normal.

Here resulting z - score is positive so option A is incorrect.

b. p( p^ >= 0.30) = ?

Mean p^ = 0.26 and std. dev. = sqrt (p*(1-p) /n) = sqrt [ 0.26 * 0.74/400] = 0.0219

so Z - value = ( 0.3 - 0.26)/ 0.0219 = 1.83

Relative p - value = 0.9664

so p( p^ >= 0.53) = 1- 0.9664 = 0.0336

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