A random sample of n = 16 winter days in Denver gave a sample mean pollution index x, - 43. Previous studies show that e, = 14. For Englewood (a suburb of Denver), a random sample of ng - 13 winter days gave a sample mean pollution index of x, - 50. Previous studies show that az = 17. 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. (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 standard normal. We assume that both population distributions are approximately normal with known standard deviations. O 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? (Test the difference , - #z. 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 = 16 winter days in Denver gave a sample mean pollution index x, - 43. Previous studies show that e, = 14. For Englewood (a suburb of Denver), a random sample of ng - 13 winter days gave a sample mean pollution index of x, - 50. Previous studies show that az = 17. 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. (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 standard normal. We assume that both population distributions are approximately normal with known standard deviations. O 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? (Test the difference , - #z. Round your answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 2AGP
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Transcribed Image Text:A random sample of n, = 16 winter days in Denver gave a sample mean pollution index x, = 43. Previous studies show that a, = 14. For Englewood (a suburb of
Denver), a random sample of ng = 13 winter days gave a sample mean pollution index of x, = 50. Previous studies show that o, = 17. 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 Hạ: H1 = H2i H: M1 < H2
O Họ: H1 = H2i H: My > H2
O Họ: H - H2i H: H1 * M2
(b) What sampling distribution will you use? What assumptions are you making?
The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
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 known standard deviations.
O 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? (Test the difference 41 - 42. 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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