Explanation Calculation: A college has 522 students in its freshmen class. It was found 19.5% of surveyed students reported that they smoke cigarettes. Let p be the true proportion of the freshmen who smokes and p ^ acts as the best estimate of p. Here, p ^ be the sample proportion and it denotes the proportion of the freshmen who smokes. The test hypotheses are given below, Null hypothesis: H 0 : p = 0.25 That is, the proportion of the freshmen who smoke is 25%. Alternative hypothesis: H A : p > 0.25 That is, the proportion of the freshmen who smoke is more than 25%. Conditions for hypotheses test: For a given dataset, the hypotheses test for a given characteristic can be conducted reasonably, if some conditions are satisfied. Conditions: Independence assumption: The selected sample should be independent and sample should be selected at random to ensure independence. 10% condition: The size of the sample drawn should be less than 10% of the population. Success/failure condition: : n p ^ ≥ 10 , n q ^ ≥ 10 Where, n be the sample size, p ^ be the sample proportion of interest and q ^ = 1 − p ^ . Verify the conditions: Independence assumption: The probability of finding a smoker student does not affect the probability of finding another. The samples taken from the freshmen class are independent. However, the sample was taken by considering the freshman class. Since there is likely to be a relationship between smoking, socio economic status and college attendance, this may not be a representative sample. 10% condition: Here, the size of freshmen class 522 which is less than the 10% population of all teenagers. Success/failure condition: n p ^ ≥ 10 and n q ^ ≥ 10 n p ^ ≥ 10 n p ^ = ( 522 ) ( 0.195 ) = 101

4th Edition

ISBN: 9780321825278

Author: Richard D. De Veaux, Paul F. Velleman, David E. Bock

Publisher: PEARSON

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Chapter R, Problem 5.23RE

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Check whether it is likely that more than 25% of freshmen are smokers.

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