The average size of single-family homes in the U. S. is 2,390 square feet. A random sample of 100 homes in California yielded the mean of 2,507 square feet and the standard deviation of 257 square feet. Do the sample data provide sufficient evidence to conclude that the mean size of California homes exceeds the national average? Test using significance level of 0.01. (7 Points)

The decision rule is

Reject the null hypothesis

The conclusion is  

There is sufficient evidence to conclude that the  mean size of California homes exceeds the national average

Step-by-step explanation:

From the question we are told that

    The  population  mean is    

    The sample size is  n  =  100

     The sample mean is  

      The standard deviation is  

      The level of significance 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  4.55  is  

From the value obtained we see that   hence

The decision rule is

Reject the null hypothesis

The conclusion is  

There is sufficient evidence to conclude that the  mean size of California homes exceeds the national average