Question

The table below contains the overall miles per gallon (MPG) of a type of vehicle. Complete parts a and b below. 21 32 20 20 31 20 25 35 34 25 45 32 26 30 a. Construct a 99% confidence interval estimate for the population mean MPG for this type of vehicle, assuming a normal distribution. The 99% confidence interval estimate is from MPG to MPG Round to one decimal place as needed.) b. Interpret the interval constructed in (a). Choose the correct answer below. 0 A. O B. ° C. D. We have 99% confidence that the population mean MPG of this type of vehicle is contained in the interval We have 99% confidence that the mean MPG of this type of vehicle for the sample is contained in the interval. 99% of the sample data fall between the limits of the confidence interval. The mean MPG of this type of vehicle for 99% of all samples of the same size is contained in the interval.

Answer 1

For given data we have,

Sample size:14

Mean (x̄): 28.2857

Standard deviation (s): 7.23696

Degree of freedom =n - 1 = 14 -1 = 13

t critical value is 3.012

t critical value for degree of freedom 13 and confidence level 99% is 3.012(by using t table)

$\bar{x}\pm t*\frac{S}{\sqrt{n}}$

$=>28.2857\pm 3.012*\left [ \frac{7.23696}{\sqrt{14}} \right ]$

=>(22.46,34.11)