Please give a step by step process: The amounts of nicotine in Dytusoon cigarett
ID: 3436000 • Letter: P
Question
Please give a step by step process:
The amounts of nicotine in Dytusoon cigarettes have a mean of 0.941 g and a standard deviation of 0.313 g. The Huntington Tobacco Company, which produces Dytusoon cigarettes, claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 40 cigarettes with a mean nicotine amount of 0.882 g.
a) Assuming that the given mean and standard deviation have not changed, find the probability of randomly selectin 40 cigarettes with a mean of 0.882 g or less.
b) Based on the result from part a), is it valid to claim that the amount of nicotine is lower? Why or why not?
Explanation / Answer
Set Up Hypothesis
Null Hypothesis H0, the amount of nicotine is same: U=0.941
Alternate Hypothesis,the amount of nicotine is lower H1: U<0.941
Test Statistic
Population Mean(U)=0.941
Given That X(Mean)=0.882
Standard Deviation(S.D)=0.313
Number (n)=40
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=0.882-0.941/(0.313/Sqrt(40)
Zo =-1.1922
| Zo | =1.1922
Critical Value
The Value of |Z ?| at LOS 0.05% is 1.64
We got |Zo| =1.1922 & | Z ? | =1.64
Make Decision
Hence Value of |Zo | < | Z ? | and Here we Do not Reject Ho
P-Value : Left Tail - Ha : ( P < -1.1922 ) = 0.1166
Hence Value of P0.05 < 0.1166, Here We Do not Reject Ho
It is valid to claim that the amount of nicotine is lower