H 0 : = 20, H a : < 20 The reduction in cholesterol level after eating a certain

Question

H0: = 20, Ha: < 20

The reduction in cholesterol level after eating a certain brand of oatmeal for breakfast for one month in people with cholesterol levels over 200 is Normally distributed, with mean (in milligrams) and standard deviation = 8. Although the brand advertises that eating their oatmeal for breakfast daily for one month will produce a mean decrease in cholesterol of more than 20 points for people with cholesterol levels over 200, you believe that the mean decrease in cholesterol is actually less than advertised. To explore this, you test the hypotheses

H0: = 20, Ha: < 20

at the 0.05 level. You will do this by randomly selecting 144 people with cholesterol levels over 200 and, after eating this brand of oatmeal for one month, computing the mean decrease in cholesterol levels of the subjects. If you observe a sample mean cholesterol reduction of = 18.52, the P-value obtained is:

between 0.01 and 0.025. between 0.025 and 0.5. between 0.05 and 0.10. less than 0.01.

Explanation / Answer

Set Up Hypothesis
Null Hypothesis H0: U=20
Alternate Hypothesis H1: U<20
Test Statistic
Population Mean(U)=20
Given That X(Mean)=18.52
Standard Deviation(S.D)=8
Number (n)=144
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=18.52-20/(8/Sqrt(144)
Zo =-2.22
| Zo | =2.22
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =2.22 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Left Tail - Ha : ( P < -2.22 ) = 0.0132
Hence Value of P0.05 > 0.0132, Here we Reject Ho

[ANSWER]
between 0.01 and 0.025.

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