7 studies show that or=19. For Englewood (a suburb of Denver), a random sample of m² = 16 winter days gave a sample mean pollution index of x = 35. Previous studies show that o2 = 15. 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: μι = μ ; Η: μ . #με Ημι-μzΗμι< με Hb: μι < μ ; Η: μ + = 3 μεM:μι>με Ho: μL 1 = (ii) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that both population distributions are approximately normal with

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Chapter1: Starting With Matlab
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-3
-2
-1
0
1
are statistically significant.
are not statistically significant.
lower limit
upper limit
-3
-2
(b) Find a 99% confidence interval for
μl 1-μl 2.
(Round your answers to two decimal places.)
-1
(iv) Based on your answers in parts (i)-(iii), will you reject or fail to reject the null hypothesis? Are the data
statistically significant at level a?
0
At the x = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically
significant. At the x = 0.01 level, we fail to reject the null hypothesis and conclude the data are not
statistically significant. At the x = 0.01 level, we reject the null hypothesis and conclude the data
At the x = 0.01 level, we reject the null hypothesis and conclude the data
1
(v) Interpret your conclusion in the context of the application.
Reject the null hypothesis,
Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution
index for Englewood and Denver. Fail to reject the null hypothesis, there is sufficient evidence that
there is a difference in mean pollution index for Englewood and Denver.
there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
O Reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution
index for Englewood and Denver.
Explain the meaning of the confidence interval in the context of the problem.
Because the interval contains only positive numbers, this indicates that at the 99% confidence level, the
mean population pollution index for Englewood is greater than that of Denver. Because the interval
contains both positive and negative numbers, this indicates that at the 99% confidence level, we can not
Q
say that the mean population pollution index for Englewood is different than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99%
confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains only negative numbers, this indicates that at the 99% confidence level, the
mean population pollution index for Englewood is less than that of Denver.
Transcribed Image Text:-3 -2 -1 0 1 are statistically significant. are not statistically significant. lower limit upper limit -3 -2 (b) Find a 99% confidence interval for μl 1-μl 2. (Round your answers to two decimal places.) -1 (iv) Based on your answers in parts (i)-(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? 0 At the x = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the x = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the x = 0.01 level, we reject the null hypothesis and conclude the data At the x = 0.01 level, we reject the null hypothesis and conclude the data 1 (v) Interpret your conclusion in the context of the application. Reject the null hypothesis, Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver. Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver. there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver. O Reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver. Explain the meaning of the confidence interval in the context of the problem. Because the interval contains only positive numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver. Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, we can not Q say that the mean population pollution index for Englewood is different than that of Denver. Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver. Because the interval contains only negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is less than that of Denver.
17
A random sample of m = 14 winter days in Denver gave a sample mean pollution index x₁ = 43. Previous
studies show that o₁ = 19. For Englewood (a suburb of Denver), a random sample of m2 = 16 winter days
gave a sample mean pollution index of x₂ = 35. Previous studies show that o2 = 15. 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.
(1) What is the level of significance?
State the null and alternate hypotheses.
Ho: L1= 2; H₁: μl μ
H2i H₁ H₁ HL ₂
Ho: L1= 2; H₁: μL 1 < μL 2
(ii) What sampling distribution will you use? What assumptions are you making?
The standard normal. We assume that both population distributions are approximately normal with
J
unknown standard deviations. The Student's t. We assume that both population distributions are
approximately normal with known 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 unknown standard
deviations.
What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate.
(Test the difference μ1-2. Round your answer to two decimal places.)
(iii) Find (or estimate) the P-value. (Round your answer to four decimal places.)
-3
Ho:μι < με Η:μι = μ 2
Sketch the sampling distribution and show the area corresponding to the P-value.
-2
-1
0
1
Ho: μL 1 =
-3 -2
-1
0 1
Transcribed Image Text:17 A random sample of m = 14 winter days in Denver gave a sample mean pollution index x₁ = 43. Previous studies show that o₁ = 19. For Englewood (a suburb of Denver), a random sample of m2 = 16 winter days gave a sample mean pollution index of x₂ = 35. Previous studies show that o2 = 15. 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. (1) What is the level of significance? State the null and alternate hypotheses. Ho: L1= 2; H₁: μl μ H2i H₁ H₁ HL ₂ Ho: L1= 2; H₁: μL 1 < μL 2 (ii) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that both population distributions are approximately normal with J unknown standard deviations. The Student's t. We assume that both population distributions are approximately normal with known 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 unknown standard deviations. What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate. (Test the difference μ1-2. Round your answer to two decimal places.) (iii) Find (or estimate) the P-value. (Round your answer to four decimal places.) -3 Ho:μι < με Η:μι = μ 2 Sketch the sampling distribution and show the area corresponding to the P-value. -2 -1 0 1 Ho: μL 1 = -3 -2 -1 0 1
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