(a) Construct a 95% confidence interval for mean, the true mean miles per gallon

Question

(a) Construct a 95% confidence interval for mean, the true mean miles per gallon for this vehicle.
(b) What assumptions are required for the interval of part (a) to be statistically valid? Are these assumptions reasonably satisfied? Explain.

iency. Computers in some vehicles cal- rious quantities related to performance. One s the fuel efficiency, or gas mileage, usually of thessed as miles per gallon (mpg). For one vehicle culate various d in this way, the miles per gallon were recorded equme the gas tank was filled, and the computer was ch eset. Here are the mpg values for a random le of 20 of these records: MPG 36.6 37.3 34.2 45.0 48.0 43.2 47.7 42.2 2 44.6 48.4 46.4 46.8 39.2 37.3 43.5 44.3 43.3 43. ose that the standard deviation is known to be 3.5 mpg.

Explanation / Answer

Sol:

to construct conidence interval we need

samlpe mean,

sample size

pop std,dev

and z crit

here sample mean=863.4/20=43.17

sample size=n=20

pop sd=3.5

z crit for 95%=1.96

95% con dence interval for , the true mean miles per gallon for this vehicle

are

sample mean-z(pop sd/sqrt(n), sample mean+z(pop sd/sqrt(n)
43.17-1.96*3.5/sqrt(20),   43.17+1.96*3.5/sqrt(20)

41.64,44.70

lower limit=41.64

upper limit=44.70

We are 95% confident that the  true mean miles per gallon for this vehicle lies in between

41.64 and 44.70

Solutiob:

Conditions are

Simple random sample

Normal distribution,n>30

Independent.

Given it srandom sample of 20 records.

meanis appoximately equal to median

Data comes from normal distribution

Assumptions are fairly satisfied

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