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 .05 level of significance and determine whether or not the average room price is significantly different from $108.50.

The decision rule is  

Fail to reject the null hypothesis

The conclusion is  

There is no sufficient evidence to show that the average room price is significantly different from $108.50

Step-by-step explanation:

From the question we are told that

   The sample size is  n = 64

    The average price is  

    The population standard deviation is  

     The level of significance is  

    The population mean is  

The null hypothesis is  

The alternative hypothesis is  

Generally the test statistics is mathematically represented as

=>      

=>    

From the z table  the area under the normal curve to the left corresponding to  1.75  is  

Generally  p-value is mathematically represented as

=>    

=>    

From the values obtained we see that   hence

The decision rule is  

Fail to reject the null hypothesis

The conclusion is  

There is no sufficient evidence to show that the average room price is significantly different from $108.50