An automobile club reported that the average price of regular gasoline in a certain state was $2.61 per gallon. The following data show the price per gallon of regular gasoline for 15 randomly selected stations in the state. Complete parts a through c below. 2.69 2.51 2.54 2.72 2.55 2.57 2.59 2.73 2.67 2.72 2.66 2.59 2.66 2.52 2.55 a. Construct a 99% confidence interval to estimate the average price per gallon of gasoline in the state. The 99% confidence interval to estimate the average price per gallon of gasoline in the state is from $ nothing to $ nothing. (Round to the nearest cent.)

So on this case the 99% confidence interval would be given by (2.56;2.68)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

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)

In order to 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 0.99 or 99%, 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(0.005,14)".And we see that

Now we have everything in order to replace into formula (1):

So on this case the 99% confidence interval would be given by (2.56;2.68)    

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step-by-step explanation: