Question

A random sample of *n*_{1} = 14 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} = 37. Previous studies
show that *σ*_{2} = 17. 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.

(i) What is the level of significance?

State the null and alternate hypotheses.

*H*_{0}: μ_{1} = μ_{2};
*H*_{1}: μ_{1} < μ_{2}

*H*_{0}: μ_{1} = μ_{2};
*H*_{1}: μ_{1} >
μ_{2}

*H*_{0}: μ_{1} = μ_{2};
*H*_{1}: μ_{1} ≠ μ_{2}

*H*_{0}: μ_{1} < μ_{2};
*H*_{1}: μ_{1} = μ_{2}

(ii) What sampling distribution will you use? What assumptions are you making?

The Student's *t*. We assume that both population
distributions are approximately normal with unknown standard
deviations.

The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.

The standard normal. We assume that both population distributions are approximately normal with known standard deviations.

The Student's *t*. We assume that both population
distributions are approximately normal with known standard
deviations.

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.)

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

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

Answer #1

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