A researcher wants to provide evidence that the mean blood cholesterol ofyoung o

Question

A researcher wants to provide evidence that the mean blood cholesterol ofyoung obese males is greater than 188 mg/dl, which is the mean blood cholesterol of all young males in general. In the researcher’s small study, the blood cholesterol levels of a random sample of 9 young obese males had a mean of 213.7 and a standard deviation of 18.5.

a) State null hypothesis and alternative hypothesis.

b) Calculate the value of the test statistic.

c) Find the p-value using the appropriate table.

d) At the .05 significance level, do you reject the null hypothesis?

e) What conclusion can you draw from the results of the test?

Explanation / Answer

Given that,
population mean(u)=188
sample mean, x =213.7
standard deviation, s =18.5
number (n)=9
null, Ho: =188
alternate, H1: >188
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.86
since our test is right-tailed
reject Ho, if to > 1.86
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =213.7-188/(18.5/sqrt(9))
to =4.168
| to | =4.168
critical value
the value of |t | with n-1 = 8 d.f is 1.86
we got |to| =4.168 & | t | =1.86
make decision
hence value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > 4.1676 ) = 0.00157
hence value of p0.05 > 0.00157,here we reject Ho
ANSWERS
---------------
null, Ho: =188
alternate, H1: >188
test statistic: 4.168
critical value: 1.86
decision: reject Ho
p-value: 0.00157
we have evidence to support mean blood cholesterol ofyoung obese males is greater than 188 mg/dl

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