The weights of soy patties sold by Veggie Burgers Delight ar

The weights of soy patties sold by Veggie Burgers Delight are normally distributed. A random sample of 18 patties yields a mean weight of 3.72 ounces with a sample standard deviation 0.6 ounces. At the .05 level of significance, perform a hypothesis test to see it the true mean weight is is less than 4 ounces. What is the standard error of the mean? What is the null hypothesis? Is the alternative one - or two-sided? What is the value of the test statistic? What is the P-value of the test statistic? What do you conclude at alpha = .05?

Solution

Set Up Hypothesis
Null, H0: U=4
Alternate, H1: U<4
Test Statistic
Population Mean(U)=4
Sample X(Mean)=3.72
Standard Deviation(S.D)=0.6
Number (n)=18
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =3.72-4/(0.6/Sqrt(18))
to =-1.98
| to | =1.98
Critical Value
The Value of |t | with n-1 = 17 d.f is 1.74
We got |to| =1.98 & | t | =1.74
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Left Tail -Ha : ( P < -1.9799 ) = 0.03207
Hence Value of P0.05 > 0.03207,Here we Reject Ho

[ANSWERS]
1. 0.1414
2. H0: U=4
3. One tail
4. to =-1.98
5. ( P < -1.9799 ) = 0.03207
6. True mean weight is less than 4