STATISTICS 101 - Written Homework Chapter 15 PartI It is believed that 44% of al

Question

STATISTICS 101 - Written Homework Chapter 15 PartI It is believed that 44% of all college students in the United States engage in binge drinking (5 or more drinks at a sitting for men, 4 or more for women). 1. Describe the population of interest College skielents engaging in binge lrinvin skuolents engaging 2. Describe the population proportion of interest in words. What value are we assuming for this propor- college stuclents tion? yy% is+ pulation Troportion of in the United Stalcs engaged in binge drinking ortion ot 3. Determine the sampling distribution for the sample proportion of students who engage in binge drink- ing from a random sample of size 2000 from this population. Make sure to check the appropriate conditions as a part of your answer. Shape - Mean Stundard deuiution- 4. In a random sample of size 2000 taken from this population, 912 college students reported engaging in binge drinking. Calculate the sample proportion.

Explanation / Answer

3)
n = 2000, p = 0.44
mean = np = 2000 * 0.44 = 880

std.dev.= sqrt(p * ( 1 -p)/n)
= sqrt(0.44 * 0.56/2000)
= 0.0111

4)
sample proportion = 912/2000 = 0.456

5)

p =0.456, n =2000
mean = np = 2000 * 0.456 = 912

std.dev.= sqrt(p * ( 1 -p)/n)
= sqrt(0.456* 0.544/2000)
= 0.0111

P(x > 912)

z = (p - mean)/s
= (912- 912)/0.0111
= 0
P(x > 912) = P(z >0) = 0.5

6)
p =0.412, n =2000
mean = np = 2000 * 0.412 = 824

std.dev.= sqrt(p * ( 1 -p)/n)
= sqrt(0.412* 0.588/2000)
= 0.011
P(x < 824)

z = (p - mean)/s
= (824- 912)/0.0111
= -7927.9279

P(x < 824) = P(z <-7927.9279) = 0

  

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