According to the National Institute on Alcohol Abuse and Alcoholism (NIAAA), and the National Institutes of Health (NIH), 41% of college students nationwide engage in binge drinking behavior, having 5 or more drinks in one occasion during the past two weeks. A college president wonders if the proportion of students enrolled at her college that binge drink is lower than the national proportion. In a commissioned study, 462 students are selected randomly from a list of all students enrolled at the college. Of these, 162 admitted to having engaged in binge drinking.1.) The college president is more interested in testing her suspicion that the proportion of students at her college that binge drink is lower than the national proportion of 0.41. Her staff tests the hypothesesHo: p = 0.41, Ha: p < 0.41. The P-value isA. between 0.05 and 0.10.B. between 0.025 and 0.05.C. between 0.01 and 0.025.D. below 0.01.

(D) The P-value is below 0.01.

Step-by-step explanation:

Test statistic (z) = (p' - p) ÷ sqrt[p(1-p) ÷ n]

p' is sample proportion = 162/462 = 0.35

p is population proportion = 0.41

n is sample size = 462

z = (0.35 - 0.41) ÷ sqrt[0.41(1-0.41) ÷ 462] = -0.06 ÷ 0.023 = -2.61

From the standard normal distribution table, the cumulative area of the test statistic is found by taking the value of 2.6 under 0.01. The value (cumulative area) is 0.9945.

The test is a one-tailed test because the alternate hypothesis is expressed using the inequality less than.

P-value = 1 - 0.9955 = 0.0045

The P-value 0.0045 is below 0.01

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0