Question

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 actually lower than the national proportion. In a commissioned study, 348 students are selected randomly from a list of all students
enrolled at the college. Of these, 132 admitted to having engaged in binge drinking.

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 .41. Her staff tests the hypotheses
H0: p = 0.41, Ha: p < 0.41.

The P-value is

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.41

H_a : p < 0.41

x = 132

n = 348

= x / n = 132 / 348 = 0.38

P₀ = 0.41

1 - P₀ = 1 - 041 = 0.59

Test statistic = z =

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

=0.38 - 0.41 / [(0.41 * 0.59) /348 ]

Test statistic = z = -1.14

P(z < -1.14)

P-value = 0.1271

= 0.05    

P-value <

Reject the null hypothesis