A random sample of n = 19 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that ơ1 = 10. For Englewood (a suburb of Denver), a random sample of nz = 18 winter days gave a sample mean pollution index of x2 = 34. Previous studies show that oz = 13. Assume the pollution index is normally distributed in both Englewood and Denver. 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. (a) What is the level of significance? State the null and alternate hypotheses. O Họ: H1 < H2; Hi: H1 = H2 O Họ: H1 = H2; Hị: µ1 * H2 O Họ: H1 = H2; Hị: µ1 > µ2 O Ho: H1 = H2; H1: µ1 < µ2 (b) What sampling distribution will you use? What assumptions are you making? O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's t. We assume that both population distributions are approximately normal with known standard deviations. O The standard normal. We assume that both population distributions are approximately normal with known standard deviations. What is the value of the sample test statistic? (Test the difference u1 - µ2. Round your answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
A random sample of n = 19 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that ơ1 = 10. For Englewood (a suburb of Denver), a random sample of nz = 18 winter days gave a sample mean pollution index of x2 = 34. Previous studies show that oz = 13. Assume the pollution index is normally distributed in both Englewood and Denver. 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. (a) What is the level of significance? State the null and alternate hypotheses. O Họ: H1 < H2; Hi: H1 = H2 O Họ: H1 = H2; Hị: µ1 * H2 O Họ: H1 = H2; Hị: µ1 > µ2 O Ho: H1 = H2; H1: µ1 < µ2 (b) What sampling distribution will you use? What assumptions are you making? O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's t. We assume that both population distributions are approximately normal with known standard deviations. O The standard normal. We assume that both population distributions are approximately normal with known standard deviations. What is the value of the sample test statistic? (Test the difference u1 - µ2. Round your answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Transcribed Image Text:A random sample of n = 19 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that o1 = 10. For
Englewood (a suburb of Denver), a random sample of n2 = 18 winter days gave a sample mean pollution index of x2 = 34. Previous studies
show that o2 = 13. Assume the pollution index is normally distributed in both Englewood and Denver. 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.
(a) What is the level of significance?
State the null and alternate hypotheses.
O Ho: H1 < l2; H1: H1 = H2
O Ho: H1 = l2; H1: H1 * H2
O Ho: H1 = l2; H1: H1 > H2
O Ho: H1 = l2; H1: H1 < µ2
(b) What sampling distribution will you use? What assumptions are you making?
O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.
O The Student's t. We assume that both population distributions are approximately normal with known standard deviations.
O The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
What is the value of the sample test statistic? (Test the difference u1 - H2. Round your answer to two decimal places.)
(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
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