Question#4 (10 marks) A College Alcohol Study finds that 67% of college students

Question

Question#4 (10 marks) A College Alcohol Study finds that 67% of college students support efforts to "crack down on underage drinking." The administration of a large college recently conducted a SRS (simple random sample) of 100 students and found that 59 of them support the crackdown on underage drinking. a) What is the sample proportion who support a crackdown on underage drinking? b) Assuming that the proportion of all the students on the campus who support a crackdown is also 67%, what is the probability that the proportion in an SRS of 100 students is less than or equal to the proportion found in the administration's sample? Be sure to check all necessary conditions required for your calculation. c Based on your calculations in part b', what can you say about your assumption? Explain

Explanation / Answer

a)

sample proportion = X/n

here X = 59 , n = 100

p^ = 59/100 = 0.59

b)

P(p^ < 0.59)

Z = (p^ - p)/sqrt(pq/n) , here p = 0.67

P(p^ < 0.59)

= P(Z < (0.59 - 0.67)/(sqrt(0.67*0.33/100))

=P(Z < -1.7013576)

= =NORMSDIST(-1.7013576) {from excel}

c)

since the 0.044438 < 0.05

we can say that the assumption is incorrect

there is sufficient evidence that proportion is less than 67 %

0.044438

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