Question

The file Sedans contains the overall miles per gallon (MPG) of 2013 midsized sedans:

38,26,30,26,25,27,22,27,39,24,24,26,25,23,25,26,31,26,37,22,29,25,33,21,21

Source: Data extracted from "ratings," Consumer Reports, April 2013, pp. 30-31.

A) Construct a 95% confidence interval estimate for the population mean MPG of 2013 family sedans, assuming a normal distribution.

B) Interpret the interval constructed in (a).

C) Compare the results in (a) to those in Problem 8.20(a).

Answer 1

The mean is calculated using

for the given sample 21, 21, 22, 22, 23, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 26, 27, 27, 29, 30, 31, 33, 37, 38, 39

And standrd deviation as

S=5.028

A) Confidence Interval calculator:

Since here sample size is 25<30 and also sample standard deviation is available so we use t-statistic:

The formula for estimation is:

μ = ± t(s_M)

where:

= sample mean
t = t statistic determined by confidence level
s_M = standard error = √(s²/n)

= 27.12
t = 2.06
s_M = √(5.028²/25) = 1.01

μ = ± t(s_M)
μ = 27.12 ± 2.06*1.01
μ = 27.12 ± 2.0755

95% CI [25.0445, 29.1955].

b) Interpretation:

I can be 95% confident that the population mean (μ) falls between 25.0445 and 29.1955.

C) Problem 8.20 is not available here.

T-table used for t-value calculation is