An officer states that the average fine levied by the safety

An officer states that the average fine levied by the safety office against companies is at most $200. A company owner suspects it is higher. She samples 10 companies and finds that the average is $210. The standard deviation of the sample is 16. Test the claim that the average is higher than $200. At = 0.05, which of the following is true?

The critical value is 1.761.

The critical value is 1.812.

Reject the null hypothesis.

There is not enough evidence to support the claim.

Solution

Set Up Hypothesis
Null, H0: U=200
Alternate, H1: U>200
Test Statistic
Population Mean(U)=200
Sample X(Mean)=210
Standard Deviation(S.D)=16
Number (n)=11
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =210-200/(16/Sqrt(11))
to =2.073
| to | =2.073
Critical Value
The Value of |t | with n = 10 d.f is 1.812 OR [ Few professors find Crical value at n-1=9 d.f is 1.822 ]
We got |to| =2.073 & | t | =1.812
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Right Tail - Ha : ( P > 2.0729 ) = 0.03248
Hence Value of P0.05 > 0.03248,Here we Reject Ho

[ANSWER]
b.  
The critical value is 1.812.
c.  
Reject the null hypothesis