Question

1) What Is Significant? Padme checks her car’s gas mileage
every time she fills up the tank.

Usually it comes out to about 28 miles per gallon, give or
take 3 miles per gallon.

a) This week Padme calculates the mileage from her last tank
of gas as being 24 MPG. Should she attribute this to normal
fluctuations in her mileage, or should she consider this
statistically significant and suspect that something’s going on
with her car? [.5 point]

b) Next week Padme calculates the mileage from her last tank
of gas as being 19 MPG. Should she attribute this to normal
fluctuations in her mileage, or should she consider this
statistically significant and suspect that something’s going on
with her car? [.5 point]

Answer #1

**1.**

From this question we can see that Padme's car's gas mileage on average is 28 miles per gallon with standard deviation 3 miles per gallon.

Now we know that if a data point falls within 3 standard deviation distance from average then it is considered as a normal fluctuation otherwise the difference from the average would be statistically significant.

**(a)** In this case, we can see that her mileage
is within 2 times standard deviation away from the average mileage.
So, she should attribute this as normal fluctuations.

**(b)** In this case, we can see that her mileage
is 3 times standard deviation away from the average mileage. So,
she should consider this statistically significant.

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