Answer to Question #181090 in Statistics and Probability for Jii

Question

A researcher claims that 75% of college students would rather spend their money for mobile phone loads than cigarettes. Another researcher would like to verify this claim. She randomly selected 400 college students. Two hundred ninety-six of these 400 students said that they would rather spend their extra money on mobile phone loads than cigarettes. At 0.05 level of confidence, is there enough evidence to conclude that the percentage of students who would rather spend their extra money for mobile phone loads than cigarettes is different from 75%.

Answer 1

$\mu$ = 400$\times$0.75 = 300

0.05$\times$300 = 15, so 300$\pm$$\frac{15}{2}$= 300$\pm7.5$ = [293 to 308]

296 ∈ [293 to 308]

Answer: it is not enough evidence to conclude that the percentage of students who would rather spend their extra money for mobile phone loads than cigarettes is different from 75%.