Example 3.6. The NCHS reported that the mean total cholesterol level in 2002 for
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Question
Example 3.6. The NCHS reported that the mean total cholesterol level in 2002 for all adults was 203. Suppose a new drug is proposed to lower total cholesterol, and a study is designed to evaluate the efficacy of the drug in lowering cholesterol. Fifteen patients are enrolled in the study and asked to take the new drug for 6 weeks. At the end of 6 weeks, each patient's total cholesterol level is measured and the sample statistics are as follows: n=15,.. 1959, and s-28.7. Is there statistical evidence of a reduction in mean total cholesterol in patients after using the new drug for 6 weeks?Explanation / Answer
Given that,
population mean(u)=203
sample mean, x =195.9
standard deviation, s =28.7
number (n)=15
null, Ho: =203
alternate, H1: !=203
level of significance, = 0.01
from standard normal table, two tailed t /2 =2.977
since our test is two-tailed
reject Ho, if to < -2.977 OR if to > 2.977
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =195.9-203/(28.7/sqrt(15))
to =-0.958
| to | =0.958
critical value
the value of |t | with n-1 = 14 d.f is 2.977
we got |to| =0.958 & | t | =2.977
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != -0.9581 ) = 0.3543
hence value of p0.01 < 0.3543,here we do not reject Ho
ANSWERS
---------------
null, Ho: =203
alternate, H1: !=203
test statistic: -0.958
critical value: -2.977 , 2.977
decision: do not reject Ho
p-value: 0.3543
there is no evidence of a reduction in mean total cholesterol in patients
after using the new drug for 6 weeks
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