Question

Compute in excel

A random sample of six cars from a particular model year had the fuel consumption figures, measure in miles per gallon, shown below. (i) Using T.INV, find a 90% confidence interval for the population mean of fuel consumption for cars of this model year. Assume the distribution is normal. (Round to 2 digits, since our raw data below are expressed with one digit.) (Show work in space provided.) (ii) Calculate the same interval using CONFIDENCE.T. (Show work in space provided.) (iii) Calculate the same interval using T.INV.2T. (Note: when calculating the lower and upper bounds of the interval, do not use a rounded mean that you’ve calculated with AVERAGE. Use the unrounded mean. Round only the final answers, which are the lower and upper bounds of the interval. Also, make sure to use STDEV.S to calculate the sample standard deviation.) Data: 28.6 18.4 19.2 25.8 19.4 20.5

Answer 1

(i)

Step 1: Store the data in C4:C9

Step 2: Find sample mean using "=AVERAGE(C4:C9)"

Step 3: Find sample sd using "=STDEV.S(C4:C9)"

Step 4: Find t(0.05,5) using "=T.INV(0.95,5)"

Step 5: Find margin of error using "=F6*F5/SQRT(F3)"

Step 6:

90% confidence interval for the population mean:

Find lower limit using "=ROUND(F4-F7,2)"

Find upper limit using "=ROUND(F4+F7,2)"

90% confidence interval for the population mean of fuel consumption for cars

=(18.54 miles per gallon , 25.43 miles per gallon )

(ii)

Step 1: Store the data in C4:C9

Step 2: Find sample mean using "=AVERAGE(C4:C9)"

Step 3: Find sample sd using "=STDEV.S(C4:C9)"

Step 4: Find margin of error using "=CONFIDENCE.T(0.1,F5,F3)"

Step 5:

90% confidence interval for the population mean:

Find lower limit using "=ROUND(F4-F14,2)"

Find upper limit using "=ROUND(F4+F14,2)"

90% confidence interval for the population mean of fuel consumption for cars

=(18.54 miles per gallon , 25.43 miles per gallon )

(iii)

Step 1: Store the data in C4:C9

Step 2: Find sample mean using "=AVERAGE(C4:C9)"

Step 3: Find sample sd using "=STDEV.S(C4:C9)"

Step 4: Find t(0.05,5) using ""=T.INV.2T(0.1,5)""

Step 5: Find margin of error using "=F21*F5/SQRT(F3)"

Step 6:

90% confidence interval for the population mean:

Find lower limit using "=ROUND(F4-F22,2)"

Find upper limit using "=ROUND(F4+F22,2)"

90% confidence interval for the population mean of fuel consumption for cars

=(18.54 miles per gallon , 25.43 miles per gallon )

Excel File: