A recent survey of gasoline prices indicated that the nation

A recent survey of gasoline prices indicated that the national average was $4.098 per gallon. The Dallas Automobile Club claimed that gasoline in Texas was significantly lower than the national average. A survey covering 10 different suburbs in Dallas found the average price of gasoline to be $3.924 per gallon with a population standard deviation of $0.053. Test the claim using = 0.01 ?

I worked the equation out and got -10.38. I don\'t understand how you get the final answer of -2.33? I know you have to find it in the table but I can\'t figure out how to read it right.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   4.098  
Ha:    u   <   4.098  
              
As we can see, this is a    left   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    3.924          
uo = hypothesized mean =    4.098          
n = sample size =    10          
s = standard deviation =    0.053          
              
Thus, t = (X - uo) * sqrt(n) / s =    -10.38181722  
Thus, getting the critical t,              
df = n - 1 =    9          
tcrit =    -   2.821437925      

      
              
              
Comparing |t| > 2.8214, we   REJECT THE NULL HYPOTHESIS.          
              
There is significant evidence that gasoline in Texas was significantly lower than the national average.

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Hi! I also got t = -10.38.

However, the -2.33 you may be talking about is the critical value (tcrit) [it seems that the other answerer used a z table instead of t.]

To get the critical value, use a t table, then look at df = 9, with level of significance 0.01 for a one tailed test. You will get -2.8214 there.

Then, as t < -2.8214, we reject Ho.