Question

A recent study found that 43% of college students engage in binge drinking (5 drinks at a sitting for men, 4 for women). After hearing of the result, a professor surveyed a random sample of 295 students at his college and found that 115 admitted to binge drinking in the last week. Should he be surprised at this result? Explain Select the correct choice below and fill in the answer box to complete your choice (Round to three decimal places as needed.) OA. No, because the observed proportion of is less than 2 standard deviations above the survey result OB. Yos, because the observed proportion of is greater than 2 standard deviations below the survey result O C . Yes, because the observed proportion of is greater than 2 standard deviations above the survey result OD. No, because the observed proportion of is less than 2 standard deviations below the survey result,

Answer 1

Standard deviation of sample proportion = $\sqrt{0.43*0.57/295}$ = 0.0288

Hence,

Range of 2 standard deviations

(0.43 - 0.029, 0.43 + 0.029)

(0.401, 0.459)

Sample proportion = 115/295 = 0.390

Hence,

Option B; 0.390