Question

Suppose a study reports that the average price for a gallon of self-serve regular unleaded gasoline is $3.76. You believe that the figure is higher in your area of the country. You decide to test this claim for your part of the United States by randomly calling gasoline stations. Your random survey of 25 stations produces the following prices.

$3.87	$3.89	$3.76	$3.80	$3.97
3.80	3.83	3.79	3.80	3.84
3.76	3.67	3.87	3.69	3.95
3.75	3.83	3.74	3.65	3.95
3.81	3.74	3.74	3.67	3.70

Assume gasoline prices for a region are normally distributed. Do the data you obtained provide enough evidence to reject the claim? Use a 1% level of significance. (Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places.)

The value of the test statistic is t =_____ and we fail to reject the null hypothesis.

Answer 1

Ho :   µ =   3.76  
Ha :   µ >   3.76   (Right tail test)
          
Level of Significance ,    α =    0.010  
sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   0.0889  
Sample Size ,   n =    25  
Sample Mean,    x̅ = ΣX/n =    3.7948  
          
degree of freedom=   DF=n-1=   24  
          
Standard Error , SE = s/√n =   0.0889/√25=   0.0178  
t-test statistic= (x̅ - µ )/SE =    (3.7948-3.76)/0.0178=   1.96
          
critical t value, t* =        2.4922   [Excel formula =t.inv(α/no. of tails,df) ]
          
p-Value   =   0.0310   [Excel formula =t.dist(t-stat,df) ]
Decision:   p-value>α, Do not reject null hypothesis       
Conclusion: There is not enough evidence that true mean is higher than 3.76

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