Statistics AP question?!!!?

I assume a normal distribution.

A 95% confidence interval means that the area under the normal dist. graph is 47.5% above the mean and 47.5 below the mean.

From the normal dist. tables this occurs at 1.96 standard deviations from the mean.

You want 1.96 x 1.3 = 2.548, above and below the mean.

So you can be 95% certain that the gas consumption is between 9.2 - 2.548 and 9.2 + 2.548 mpg.

These limits are 6.652 mpg and 11.748 mpg.

EDIT

I will refer to the number of fords sampled as "n" and the number of fords in the population as "N"

First of all, we see that this is a t distribution, not a z distribution because we don't know the true population standard deviation.

A confidence interval is used in statistics to estimate the true mean of the population.

Before you can create any confidence intervals, you need to confirm that these data are an SRS of the population and therefore are representative of it, that each ford had about an equal chance of being chosen (independent sampling) and that the sample distribution is normal.

1) It does not state in the question that these were chosen through an SRS, so you may not be able to generalize to the population.

2) You can assume independent sampling if there were more than n*10 or 100 Ford Excursions made (assume that there were if it isn't stated in the problem). n*10 ≤N is used because to give each ford an about equal chance of being chosen you need to sample no more than 10% of the population.

3) Normality: If n is 15 or greater then you can make a graph of the data and if they appear relatively normal then you can use the t procedure. If n is over 30 then you can use the t procedure no matter what the data look like. If n is 10, then you must make a graph of the data and if they appear normal with only minor skews and no outliers, then you can assume normality. If you don't have the data, then you aren't sure if the data are normal.

n=10

x bar=9.2

Sx=1.3

x bar±(t*)(Sx/sqrt(n))

t* for a 95% confidence interval with n=10 would be 2.262. To find this, look in table c(it should be at the back of your book) and look for n-1, or 9 at in the left column and 95% at the bottom.

Your confidence interval will be 9.2±2.262(1.3/sqrt10) or 9.2± 0.929899369, giving you [8.27010063,10.1298994]

To answer, you say "We are 95% confident that the true mean gas mileage of the new Ford Excursions is between 8.27010063 and 10.1298994".