A health administration recommends that individuals consume 1000 mg of calcium d

Question

A health administration recommends that individuals consume 1000 mg of calcium daily. After an advertising campaign aimed at male teenagers, a dairy association states that male teenagers consume more than the recommended daily amount of calcium. To support this statement, the association obtained a random sample of 50 male teenagers and found that the mean amount of calcium consumed was 1010 mg, with a standard deviation of 120 mg. Is there significant evidence to support the statement of the association at the alpha equals0.05 level of significance? Find the test statistic? Find the P-Value.

Explanation / Answer

Given that,
population mean(u)=1000
sample mean, x =1010
standard deviation, s =120
number (n)=50
null, Ho: =1000
alternate, H1: !=1000
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.01
since our test is two-tailed
reject Ho, if to < -2.01 OR if to > 2.01
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =1010-1000/(120/sqrt(50))
to =0.589
| to | =0.589
critical value
the value of |t | with n-1 = 49 d.f is 2.01
we got |to| =0.589 & | t | =2.01
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != 0.5893 ) = 0.5584
hence value of p0.05 < 0.5584,here we do not reject Ho
ANSWERS
---------------
null, Ho: =1000
alternate, H1: !=1000
test statistic: 0.589
critical value: -2.01 , 2.01
decision: do not reject Ho
p-value: 0.5584
there is significant evidence to support the statement of the association at the alpha equals

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