In order to determine the average price of hotel rooms in At

In order to determine the average price of hotel rooms in Atlanta, a sample of 64 hotels was selected. It was determined that the average price of the rooms in the sample was $112. The population standard deviation is known to be $16. Use a 0.05 level of significance and determine whether or not the average room price is significantly different from $108.50. Use both p-value and ciritical value methods.

Please answe the following,

What is the Null Hypothesis?

The Alternative Hypothesis?

Analysis & Decision based on p-Value

Analysis & Decision based on Critical value

Solution

Set Up Hypothesis
Null Hypothesis H0: U=108.5
Alternate Hypothesis H0: U=108.5
Test Statistic
Population Mean(U)=108.5
Given That X(Mean)=112
Standard Deviation(S.D)=16
Number (n)=64
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=112-108.5/(16/Sqrt(64)
Zo =1.75
| Zo | =1.75
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =1.75 & | Z | =1.96
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value : Two Tailed ( double the one tail ) - Ha : ( P != 1.75 ) = 0.0801
Hence Value of P0.05 < 0.0801, Here We Do not Reject Ho

What is the Null Hypothesis?
H0: U=108.5

The Alternative Hypothesis?
H0: U=108.5

Analysis & Decision based on p-Value?
Value of P0.05 < 0.0801, Here We Do not Reject Ho

Analysis & Decision based on Critical value?
Value of |Zo | < | Z | and Here we Do not Reject Ho