A random sample of n_1 = 14 winter days in Denver gave a sample mea

Chesley

Chesley

Answered question

2021-10-26


A random sample of n1=14 winter days in Denver gave a sample mean pollution index x1=43.
Previous studies show that σ1=19.
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=13.
Assume the pollution index is normally distributed in both Englewood and Denver.
(a) State the null and alternate hypotheses.
H0:μ1=μ2;μ1>μ2
H0:μ1<μ2;μ1=μ2
H0:μ1=μ2;μ1<μ2
H0:μ1=μ2;μ1μ2
(b) What sampling distribution will you use? What assumptions are you making?
The Students

Answer & Explanation

Anonym

Anonym

Skilled2021-10-27Added 108 answers

Step 1
Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are solving the first 3 parts for you, according to our policy. If you need help with any of the other parts, please re-post the question and mention the part you want to be answered. Step 2 a) The null and alternative hypotheses are shown below: Null hypothesis:
H0:μ1=μ2 Alternative hypothesis:
H1:μ1μ2 b) Here, the assumptions are both population distributions are approximately normal with known standard deviations. Therefore, the sampling distribution will use here is the standard normal. Thus, the correct option is the standard normal. We assume that both population distributions are approximately normal with known standard deviations. c) The test statistic is obtained as follows:
z=x1x2σ12n1+σ22n2
z={43}{37}19214+13212=0.95 Thous, the value of the test statistics is 0.95.

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