Please give a step by step process The amounts of nicotine i

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?

Solution

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