3. According to the National Institute on Alcohol Abuse and Alcoholism (NIAAA) a
ID: 3151902 • Letter: 3
Question
3. 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 on one occasion during the past two weeks. A college president wonders if the proportion of students enrolled at her college who binge drink is actually lower than the national proportion. In a commissioned study, 365 students are selected randomly from a list of all students enrolled at the college. Of these, 129 admit to having engaged in binge drinking. Test the hypotheses H0:p=0.41 versus Ha:p<0.41. The P-value (±0.0001) is Use = 0.01 to make a decision about students at this college: Students at this college binge drink more than the national rate. Students at this college binge drink similarly to the national rate. Students at this college binge drink less than the national rate.
4.Starting in the 1970s, medical technology allowed babies with very low birth weight (VLBW, less than 1500 grams, about 3.3 pounds) to survive without major handicaps. It was noticed that these children nonetheless had difficulties in school and as adults. A long-term study has followed 241 VLBW babies to age 20 years, along with a control group of 237 babies from the same population who had normal birth weight. IQ scores were available for 115 men in the VLBW group. The mean IQ was 90.3, and the standard deviation was 16.9. The 107 men in the control group had mean IQ 91.9, with standard deviation 13.6. The two-sample test statistic (using the VLBW babies as group 1) is . (±0.001) Is there strong evidence (at the 0.001 level) that mean IQ is lower among VLBW men than among controls from similar backgrounds?
please help with both if possible, I am using the formula pˆ±z pˆ(1pˆ)/n for question 4 and z=pˆp0/p0(1p0)/n. if you can do step by step to show me how i am plugging in wrong I will appreciate it
Explanation / Answer
3. 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 on one occasion during the past two weeks. A college president wonders if the proportion of students enrolled at her college who binge drink is actually lower than the national proportion. In a commissioned study, 365 students are selected randomly from a list of all students enrolled at the college. Of these, 129 admit to having engaged in binge drinking. Test the hypotheses H0:p=0.41 versus Ha:p<0.41. The P-value (±0.0001) is Use = 0.01 to make a decision about students at this college: Students at this college binge drink more than the national rate. Students at this college binge drink similarly to the national rate. Students at this college binge drink less than the national rate.
Formulating the null and alternatuve hypotheses,
Ho: p <= 0.41
Ha: p > 0.41
As we see, the hypothesized po = 0.41
Getting the point estimate of p, p^,
p^ = x / n = 0.353424658
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.025743732
Getting the z statistic,
z = (p^ - po)/sp = -2.19763564
As this is a 1 tailed test, then, getting the p value,
p = 0.013987541 [ANSWER, P VALUE]
significance level = 0.01
As P > 0.01, we FAIL TO REJECT THE NULL HYPOTHESIS.
Hence, there is no significant evidence that students at this college binge drink less than the national rate at 0.01 level. [CONCLUSION]
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