The National Institutes of Health recommend that children aged 9-13 have 240 mg

Question

The National Institutes of Health recommend that children aged 9-13 have 240 mg of magnesium per day. (source: https://ods.od.nih.gov/factsheets/Magnesium- HealthProfessional). Suppose a nutritionist suspects that children in this age group do not get enough magnesium in their diet. A random sample of 16 children (aged 9-13) participate in a nutritional study, and cach day everything they eat is carefully recorded and the amount of magnesium intake is computed. Suppose the mean daily intake of magnesium, from this sample, is 228 mg, and the standard deviation from the sample is 87 mg. Is this evidence, at the 5% level of significance, that children's (aged 9-13) mean daily intake of magnesium is less than 240 mg? 1. Write the null and alternate hypotheses 2. Compute the t-score and the degrees of freedom 3. Estimate the p-value (you may use the table or a calculator), and explain what the p-value means in this context

Explanation / Answer

Given that,
population mean(u)=240
sample mean, x =228
standard deviation, s =87
number (n)=16
null, Ho: =240
alternate, H1: <240
level of significance, = 0.05
from standard normal table,left tailed t /2 =1.753
since our test is left-tailed
reject Ho, if to < -1.753
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =228-240/(87/sqrt(16))
to =-0.5517
| to | =0.5517
critical value
the value of |t | with n-1 = 15 d.f is 1.753
we got |to| =0.5517 & | t | =1.753
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :left tail - Ha : ( p < -0.5517 ) = 0.29463
hence value of p0.05 < 0.29463,here we do not reject Ho
ANSWERS
---------------
null, Ho: =240
alternate, H1: <240
test statistic: -0.5517
the value of |t | with n-1 = 15 d.f is -1.753
decision: do not reject Ho
p-value: 0.29463

we not sure that the mean intake is less than 240

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.