Question

A random sample of *n*_{1} = 10 winter days in
Denver gave a sample mean pollution index *x*_{1} =
43. Previous studies show that *σ*_{1} = 21. For
Englewood (a suburb of Denver), a random sample of
*n*_{2} = 12 winter days gave a sample mean
pollution index of *x*_{2} = 36. Previous studies
show that *σ*_{2} = 13. Assume the pollution index
is normally distributed in both Englewood and Denver.

(a) Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance.

(b) What is the level of significance?

(c) What is the value of the sample test statistic? Compute the
corresponding *z* or *t* value as appropriate. (Test
the difference μ_{1} − μ_{2}. Round your answer to
two decimal places.)

(d) Find (or estimate) the *P*-value. (Round your answer
to four decimal places.)

(e) Find a 99% confidence interval for μ_{1} −
μ_{2}. (Round your answers to two decimal places.)

lower limit | ? |

upper limit ? |

Answer #1

lower limit = -12.65

Upper limit = 26.65

A random sample of n1 = 14 winter days in
Denver gave a sample mean pollution index x1 =
43. Previous studies show that σ1 = 21. For
Englewood (a suburb of Denver), a random sample of
n2 = 12 winter days gave a sample mean
pollution index of x2 = 37. Previous studies
show that σ2 = 17. Assume the pollution index
is normally distributed in both Englewood and Denver.
(a) Do these data indicate that the mean population...

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