A Chip Company claims that there is 32 oz in every bag of ch

A Chip Company claims that there is 32 oz in every bag of chips with a specified population standard deviation of 1.5. A sample of 40 bags where weighted with an sample mean of 31.4. A consumer feels that this less than what the company claims. There is enough information to assume normality and use the standard normal probability distribution over the t-distribution.

Solution

Set Up Hypothesis
Null, H0: U=32
Alternate H1: U<32
Test Statistic
Population Mean(U)=32
Given That X(Mean)=31.4
Standard Deviation(S.D)=1.5
Number (n)=40
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=31.4-32/(1.5/Sqrt(40)
Zo =-2.53
| Zo | =2.53
Critical Value
The Value of |Z | at LOS 0.01% is 2.33
We got |Zo| =2.5298 & | Z | =2.33
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Left Tail - Ha : ( P < -2.53 ) = 0.0057
Hence Value of P0.01 > 0.0057, Here we Reject Ho

At the 1% level of significant there is suffcient evidence to reject the null hypothesis. . That is, the mean weight is less than 32 oz.