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CONSTRUCT A 90% CONFIDENCE INTERVAL OF THE AVERAGE GASOLINE PRICE PER GALLON BASED ON A RECENT...

CONSTRUCT A 90% CONFIDENCE INTERVAL OF THE AVERAGE GASOLINE PRICE PER GALLON BASED ON A RECENT SAMPLE OF 48 STATIONS. THE SAMPLE MEAN WAS $2.63. ASSUME THE POPULATION STANDARD DEVIATION IS $0.31.

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Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 2.63

Population standard deviation =    = 0.31
Sample size = n =48

At 90% confidence level the z is

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )


Margin of error = E = Z/2    * ( /n)

= 1.645 * (0.31 /  48 )

= 0.07
At 90% confidence interval mean
is,

- E < < + E
2.63 - 0.07 <   < 2.63 + 0.07

(2.56 , 2.70)

orchestra answered 1 year ago
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