Ford Motor Company is confident that its 2016 F-150 truck gets 26 miles per gall

Question

Ford Motor Company is confident that its 2016 F-150 truck gets 26 miles per gallon on the highway. Before they begin to advertise this fact they want to be 95% certain of their claim. To accomplish this, they take a random sample of 250 trucks and measure their gas mileage. The average was 24.98 mpg with a population standard deviation of 4.88 mpg. Calculate the Upper and Lower Confidence Interval values AND can Ford make the claim that their trucks will get 26 mpg on the highway.

select answ

Lower = 25.06, Upper = 26.94 & Claim is yes their trucks do get 26 mpg

Lower = 24.38, Upper = 25.58 & Claim is no their trucks do not get 26 mpg

Lower = 24.21, Upper = 25.61, & Claim is no their trucks do not get 26 mpg

Lower = 24.19, Upper = 25.71, & Claim is no their trucks do not get 26 mpg

Explanation / Answer

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 =    0.025          
X = sample mean =    24.98          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    4.88          
n = sample size =    250          
              
Thus,              
Margin of Error E =    0.604919952          
Lower bound =    24.37508005          
Upper bound =    25.58491995          
              
Thus, the confidence interval is              
              
(   24.38   ,   25.58   )

Hence, as 26 is not inside this,

OPTION B: Lower = 24.38, Upper = 25.58 & Claim is no their trucks do not get 26 mpg [ANSWER, B]

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