Question

A random sample of six cars from a particular model year had the following fuel consumption figures ( in miles per gallon). find the 98% confidence interval for the true mean fuel consumption for cars of this model year.

Sample Data: 19.3 , 18.5 , 18.4 , 20.9 , 20.7 , 18.7

Left Endpoint _____

Right Endpoint _____

Answer 1

Let's use Minitab

Here population standard deviation is not given and we have sample data set so we can used one sample t interval to construct the confidence interval for population mean.

Step 1) enter the given data set in minitab columns

Step 2) Stat>>>Basic Statistics >>1 sample t...

Click on "Samples in columns"

select the column name in which your data is present.

then click on Option select level of confidence = 98

Alternative " not equal"

Click on Ok

Again "click on OK"

then we get the following output

From the above output, we get:

Left Endpoint 18.244

Right Endpoint 20.590

One-Sample T: X Mean StDev SE Mean 95% CI 19.417 1.118 0.456 (18.244, 20.590)

Let's use formula :

The formula of t interval is as follows:

+/- E

Where E = margin of error.

Formula of E is as follows:

t_c = critical t value

se() is the standard error of sample mean.

Let's use excel for calculation:

The formulae used on the above excel-sheet are as follows: