Question

An automobile club reported that the average price of regular gasoline in a certain state was $2.83 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

2.65	2.78	2.91	2.84	2.88
2.95	2.78	2.69	2.71	2.99
2.81	2.67	2.85	2.93	2.79

a. Construct an 80​% confidence interval to estimate the average price per gallon of gasoline in the state.

Answer: ​The 80% confidence interval to estimate the average price per gallon of gasoline in the state is from ​$2.78 per gallon to ​$2.85 per gallon.

b. Do the results from this sample validate the automobile​ club's findings?

Answer: First determine whether the population​ mean, 2.83​, is contained within the 80 % confidence​ interval, which is approximately from 2.78 to 2.85.

Note that 2.83 is contained within the 80 % confidence interval.

To determine whether the results from this sample validate the automobile​ club's findings, recall that a confidence interval for the mean is an interval estimate around a sample mean that provides one with a range of where the true population mean lies.

c. What assumptions need to be made about this​ population?

Answer: Carefully review the requirements for calculating a confidence interval with the​ Student's t-distribution when the sample size is less than or equal to 30.

Above are the questions and answers. Please provide all Excel formulas (not calculations) that get to these answers.

Answer 1

a).steps in excel for getting 80% confidence interval for the population mean:-

copy the data in a column of excel data data analysis descriptive statistics okin input range select the entire data range by dragging the mousein grouped by select columns in output range select new worksheet ply tick summary statistics, confidence level for mean and type 80 in the boxok.

your excel output be:-

Column1
Mean	2.815333
Standard Error	0.027183
Median	2.81
Mode	2.78
Standard Deviation	0.10528
Sample Variance	0.011084
Kurtosis	-0.99729
Skewness	-0.02663
Range	0.34
Minimum	2.65
Maximum	2.99
Sum	42.23
Count	15
Confidence Level(80.0%)	0.036562

the 80% confidence interval be:-

[ 0.037 is the last row of your excel output, that is confidence level (80%) = 0.036562]

part b and c do not need any computations in excel.

d).we have to check normality assumption..for checking the assumption i am using boxplot.

steps in excel :-

select the entire data range insert recommended charts all chartsselect bx and whisker ok.

your excel output be:-

from the boxplot it is clear that the data is approximately normal and the sample size = 15 <303...so, we can use a ​Student's t-distribution to calculate the confidence interval .

I AM UPLOADING THE SCREENSHOT HOW YOUR EXCEL FORMAT WILL LOOK LIKE, JUST FOR YOUR EASE TO UNDERSTAND.

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