A recent study of 36 selfservice gasoline stations in the Fr

A recent study of 36 self-service gasoline stations in the Fresno area revaled a mean price of 4.02 the population standard deviation was .16

What is the point estimate for all self-service gas station prices?

What is the 94% confidence interval?

What is your conclusion

Solution

a)

The point estimate is the mean price, 4.02. [ANSWER]

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b)

Note that              
Margin of Error E = z(alpha/2) * s / sqrt(n)              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.03          
X = sample mean =    4.02          
z(alpha/2) = critical z for the confidence interval =    1.880793608          
s = sample standard deviation =    0.16          
n = sample size =    36          
              
Thus,              
Margin of Error E =    0.050154496          
Lower bound =    3.969845504          
Upper bound =    4.070154496          
              
Thus, the confidence interval is              
              
(   3.969845504   ,   4.070154496   ) [ANSWER]

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c)

We are 95% confident that the true mean price of self-service gasoline stations in the Fresno area is between 3.9698 and 4.0702. [CONCLUSION]