The amounts (in ounces) of juice in eight randomly selected juice bottles are: 15.3 15.3 15.7 15.7 15.3 15.9 15.3 15.9 Construct a 98% confidence interval for the mean amount of juice in all such bottles

The 98% confidence interval would be given by (15.26;15.84)    

Step-by-step explanation:

Notation

represent the sample mean for the sample  

population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

  (1)

We can calculate the mean and the sample deviation we can use the following formulas:  

(2)  

(3)  

The mean calculated for this case is

The sample deviation calculated

In order to calculate the critical value we need to find first the degrees of freedom, given by:

Since the Confidence is 0.98 or 98%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.01,7)".And we see that

And the confidence interval is given by:

The 98% confidence interval would be given by (15.26;15.84)