ccording to the Natonal Institute on Alcohol Abuse and Alcoholism (NIAAA), and t
ID: 2945781 • Letter: C
Question
ccording to the Natonal Institute on Alcohol Abuse and Alcoholism (NIAAA), and the Nati ral Institutes of Health (NIH), 41% of college students nation de engage r b ge rnkro be avor having five or more dnrks on one o casi n dring the past two weeks. A colege pres dent wonders the proportion of students en o ed at her college that inge 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 dmitted to having egaged in binge drinking. The college president is more interested in testing her suspicion that the proportion of students at her college that lange drink s ower than the national proportion of 0.41. Her staff tests the hypotheses Ho -0.41, Ha p 0.41, The P-valueis between 0.025 and 0.05 below 0.01 between 0.01 and 0.025 between 0.05 and 0.10 ·Accord ng to the Natwmal Institute on Alcolol Abuse ond Ak hol, (N?AM), and the Note nal i ututes of Health NIH), 41% of o-sti leres n t o o" "bing" drinking beavion, having ive or more drinks on one occasion dus binge drnk is ower than the national proportion In a comsioned study, 462 students are selected randomly from a st of all students enroled at the college Or se,1 edmitted to having engaged in binge drinking Based on the Pyalue for this test, which of the follomng conclusons is reasonable? There is strong evidence that the proportion of students at this colege that binge drink is lower than the national proportion of 0-41 w" can't reach any reasonsta, condmon because the smemption, necessary for sporicance test for·proportion-re not met-n thi, 'we There inte evidence to "apport-cor ckson that te proportion of stoder", st this parti dar caleoet' ac urge d ink " lo er than the nit, nal ?.sportu of 0.41Explanation / Answer
Solution:- Between 0.01 and 0.025
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P > 0.41
Alternative hypothesis: P < 0.41
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.
Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-score test statistic (z).
S.D = sqrt[ P * ( 1 - P ) / n ]
S.D = 0.02288
z = (p - P) / S.D
z = - 2.16
where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.
Since we have a one-tailed test, the P-value is the probability that the z-score is less than -2.16.
Thus, the P-value = 0.015
Between 0.01 and 0.025
Interpret results. Since the P-value (0.015) is less than the significance level (0.05), we cannot accept the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that the proportion of students at her college that binge drink is lower than the national proportion of 0.41.
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