A firm in Lebanon has developed a chemical solution that can be added to car gasoline which they believe will increase the miles per gallon that cars will get. The owners are interested in estimating the difference between mean mpg for cars using the chemical solution versus those that are not using the solution. The following data represent the mpg for independent random samples of cars from each population. with Solution without Solution ______________________________ n1 = 36 n2 = 42 x1 = 25.45 x2 = 24.1 _______________________________ Assume that the populations are normally distributed and the population standard deviations are known to be σ1 = 3.95 (with solution) and σ2 = 3.09 (without solution). Given this data, can the owners believe that there is a difference between mean mpg for cars using the chemical solution versus those that are not using the solution? Test using an alpha level equal to 0.05
3) A firm in Lebanon has developed a chemical solution that can be added to car gasoline
which they believe will increase the miles per gallon that cars will get. The owners are
interested in estimating the difference between mean mpg for cars using the chemical
solution versus those that are not using the solution. The following data represent the mpg
for independent random samples of cars from each population.
with Solution without Solution
______________________________
n1 = 36 n2 = 42
x1 = 25.45
x2 = 24.1
_______________________________
Assume that the populations are
deviations are known to be σ1 = 3.95 (with solution) and σ2 = 3.09 (without solution).
Given this data, can the owners believe that there is a difference between mean mpg for
cars using the chemical solution versus those that are not using the solution? Test using an
alpha level equal to 0.05.
4) Given the following null and alternative hypothesis:
H0: σ 2 ≤ 52
HA : σ 2 > 52
and the following sample information n = 24, s = 9, and α = 0.05. Using the test statistic
approach, what conclusion should be reached about the null hypothesis?
5) Two companies, A and B, produce electric light bulbs. The lifetime for the bulbs
produced at these companies are approximately normally distributed, with means of 22
hrs and 25 hrs, respectively. If we select 13 bulbs from company A and 16 bulbs from
company B and determine the standard deviations of their lifetimes to be 20 hrs and 38 hrs,
respectively, can we conclude at a 0.01 level of significance that the variability of the A bulbs
is significantly less than that of the B bulbs?
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