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Suppose we observe two independent random samples X1,...,X, with each X ~ N(1,02) and Y₁,..., Y, with each Y ~N(2,σ²). We will assume that μ1, μ₂ and σ² are unknown. We are given = 10.1, y = 7.1, s² = 5.5 and s² = 6.4, with n₁ = 13 and n₂ = 19. We would like to test the hypothesis Ho₁ = 2 versus H₁ = 11 12. What test statistic should you use? You may assume the samples come from populations with equal variances. Oa. Z= b. T= X-Y 0²√1/n₁+1/na X-Y Sov/1/n₁+1/12 ~ N(0, 1), where² = 6.04. ~t+-2, where S2 is the pooled estimate of variance. ○ c. T= d Sal√12 ~12, where d is the mean and S is the sample variance of paired differences d₁ = x - yi, i = 1,..., 13. Clear my choice Suppose we want to formally test the assumption that the variances of the two populations the samples come from are equal. What is the test statistic we should use? a. W = b. F= ○ c. W = (n-1)S ~ 5.5 ~PM-1 (n-1)S -1 ~ 6.4 We will now compute a 95% confidence interval for the ratio of 1. Here, we are no longer assuming equal variances, so σ denotes the population variance of each X, and σdenotes the population variance of each Y. What is the lower endpoint of this confidence interval? Give your answer to 3 decimal places. What is the upper endpoint of this confidence interval?

Suppose we observe two independent random samples X1,...,X, with each X ~ N(1,02) and Y₁,..., Y, with each Y ~N(2,σ²). We will assume that μ1, μ₂ and σ² are unknown. We are given = 10.1, y = 7.1, s² = 5.5 and s² = 6.4, with n₁ = 13 and n₂ = 19. We would like to test the hypothesis Ho₁ = 2 versus H₁ = 11 12. What test statistic should you use? You may assume the samples come from populations with equal variances. Oa. Z= b. T= X-Y 0²√1/n₁+1/na X-Y Sov/1/n₁+1/12 ~ N(0, 1), where² = 6.04. ~t+-2, where S2 is the pooled estimate of variance. ○ c. T= d Sal√12 ~12, where d is the mean and S is the sample variance of paired differences d₁ = x - yi, i = 1,..., 13. Clear my choice Suppose we want to formally test the assumption that the variances of the two populations the samples come from are equal. What is the test statistic we should use? a. W = b. F= ○ c. W = (n-1)S ~ 5.5 ~PM-1 (n-1)S -1 ~ 6.4 We will now compute a 95% confidence interval for the ratio of 1. Here, we are no longer assuming equal variances, so σ denotes the population variance of each X, and σdenotes the population variance of each Y. What is the lower endpoint of this confidence interval? Give your answer to 3 decimal places. What is the upper endpoint of this confidence interval?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 14PPS
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Suppose we observe two independent random samples X1,...,X, with each X ~ N(1,02) and Y₁,..., Y, with each Y ~N(2,σ²). We will assume that μ1, μ₂ and σ² are unknown. We are given = 10.1, y = 7.1, s² = 5.5 and s² = 6.4, with n₁ = 13 and n₂ = 19. We would like to test the hypothesis Ho₁ = 2 versus H₁ = 11 12. What test statistic should you use? You may assume the samples come from populations with equal variances. Oa. Z= b. T= X-Y 0²√1/n₁+1/na X-Y Sov/1/n₁+1/12 ~ N(0, 1), where² = 6.04. ~t+-2, where S2 is the pooled estimate of variance. ○ c. T= d Sal√12 ~12, where d is the mean and S is the sample variance of paired differences d₁ = x - yi, i = 1,..., 13. Clear my choice Suppose we want to formally test the assumption that the variances of the two populations the samples come from are equal. What is the test statistic we should use? a. W = b. F= ○ c. W = (n-1)S ~ 5.5 ~PM-1 (n-1)S -1 ~ 6.4 We will now compute a 95% confidence interval for the ratio of 1. Here, we are no longer assuming equal variances, so σ denotes the population variance of each X, and σdenotes the population variance of each Y. What is the lower endpoint of this confidence interval? Give your answer to 3 decimal places. What is the upper endpoint of this confidence interval?
Transcribed Image Text:Suppose we observe two independent random samples X1,...,X, with each X ~ N(1,02) and Y₁,..., Y, with each Y ~N(2,σ²). We will assume that μ1, μ₂ and σ² are unknown. We are given = 10.1, y = 7.1, s² = 5.5 and s² = 6.4, with n₁ = 13 and n₂ = 19. We would like to test the hypothesis Ho₁ = 2 versus H₁ = 11 12. What test statistic should you use? You may assume the samples come from populations with equal variances. Oa. Z= b. T= X-Y 0²√1/n₁+1/na X-Y Sov/1/n₁+1/12 ~ N(0, 1), where² = 6.04. ~t+-2, where S2 is the pooled estimate of variance. ○ c. T= d Sal√12 ~12, where d is the mean and S is the sample variance of paired differences d₁ = x - yi, i = 1,..., 13. Clear my choice Suppose we want to formally test the assumption that the variances of the two populations the samples come from are equal. What is the test statistic we should use? a. W = b. F= ○ c. W = (n-1)S ~ 5.5 ~PM-1 (n-1)S -1 ~ 6.4 We will now compute a 95% confidence interval for the ratio of 1. Here, we are no longer assuming equal variances, so σ denotes the population variance of each X, and σdenotes the population variance of each Y. What is the lower endpoint of this confidence interval? Give your answer to 3 decimal places. What is the upper endpoint of this confidence interval?
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