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9. Consider the ANOVA model where Xij ~ N(μί,02). Then show that SSE (a) the random...
Problem 2. Consider the one-way layout ANOVA model, where we assume that Yij = μί-cij,に1, . . . , I and J 1, . . . ,J,...
Problem 2. Consider the one-way layout ANOVA model, where we assume that Yij = μί-cij,に1, . . . , I and J 1, . . . ,J, where μί's are fixed unknown with zero mean treatment means and eiy's are random errors , al such that Σ-lai -0 and E[Yj-μ + ai,1- Show that there exists unique numbers μ, ai, a. b. Show that the null hypothesis Ho : μ,-...- μι is equivalent to Ho : 01 ,-. . .-a1-0...
Problem 2. Consider the one-way layout ANOVA model, where we assume that Yij = μί-cij,に1, ....
Problem 2. Consider the one-way layout ANOVA model, where we assume that Yij = μί-cij,に1, . . . , I and J 1, . . . ,J, where μί's are fixed unknown with zero mean treatment means and eiy's are random errors , al such that Σ-lai -0 and E[Yj-μ + ai,1- Show that there exists unique numbers μ, ai, a. b. Show that the null hypothesis Ho : μ,-...- μι is equivalent to Ho : 01 ,-. . .-a1-0
(1 point) In order to compare the means of two populations, independent random samples of 271...
(1 point) In order to compare the means of two populations, independent random samples of 271 observations are selected from each population, with the following results: Sample 1 Sample 2 1145 2 120 (a) Use a 99 % confidence interval to estimate the difference between the population means (A-μ). (b) Test the null hypothesis: HO : (μί-12-0 versus the alternative hypothesis. Ha : (μ-μ2)メ (i) the test statistic z () the positive critical z score (ii) the negative critical z...
Question. Consider a random sample X11-X12. . . . , Xini with ni-10 from N2(μ, Σ) and a random sa...
Question. Consider a random sample X11-X12. . . . , Xini with ni-10 from N2(μ, Σ) and a random sample X21 . X22, . . . , x2n2 with n2 10 from M2(μ2. Σ ), where μί-μί, μί21.- 1,2. The summary statistics of the two samples as follows: 10 -5 s, 10-5 and S2-5 4 1. Test the hypothesis Ho : μ,-,12 versus Hi : μί ,< μ2 at 5% significance level. Hint: Use m1 n2 where Spooled = (n-1)sit2-2...
(1 point) (Give answers to at least two decimal places. For simplicity, use the standard normal...
(1 point) (Give answers to at least two decimal places. For simplicity, use the standard normal distribution bacause the samples are both large.) In order to compare the means of two populations, independent random samples of 4 observations are selected from each population, with the following results: Sample 1 Sample 2 81 -15582-125 Use a 97 % confidence interval to estimate the difference between the population means (M1-12). -304.502 (b) Test the null hypothesis: H0 the test statistic z The...
(1 point) (Give answers to at least two decimal places. For simplicity, use the standard normal...
(1 point) (Give answers to at least two decimal places. For simplicity, use the standard normal distribution bacause the samples are both large.) In order to compare the means of two populations, independent random samples of 93 observations are selected from each population, with the following results: Sample 1 Sample 2 s1 = 170 s2 = 195 (a) Use a 98 % confidence interval to estimate the difference between the population means ( ) - Test the null hypothesis: Ho...
Suppose that independent samples of sizes n1, n2, . . . , nk are taken from each of k normally di...
Suppose that independent samples of sizes n1, n2, . . . , nk are taken from each of k normally distributed populations with means μ1,μ2, . . . , μk and common variances, all equal to σ 2. Let Yi j denote the j th observation from population i, for j = 1, 2, . . . , ni and i = 1, 2, . . . , k, and let n = n1 + n2 + ··· + nk...
Suppose that X ~ POI(μ), where μ > 0. You will need to use the following fact: when μ is not too close to 0, VR ape x N(VF,1/4). (a) Suppose that we wish to test Ho : μ-710 against Ha : μ μί a...
Suppose that X ~ POI(μ), where μ > 0. You will need to use the following fact: when μ is not too close to 0, VR ape x N(VF,1/4). (a) Suppose that we wish to test Ho : μ-710 against Ha : μ μί are given and 10 < μι. m, where 140 and Using 2 (Vx-VHo) as the test statistic, find a critical region (rejection region) with level approximately a (b) Now suppose that we wish to test Ho...
Why do we need time n when we calculate SSTR? In other words, why n times...
Why do we need time n when we calculate SSTR? In other words,
why n times (mean of a factor level - mean of
total)^2 Could you give me some intuitive explanation or
proof?
Here are my lecture notes.
Store IDs Total Mean ni S1 S2 S3 S4 S5(Y) 73 67 78 136 14.6 13.4 19.5 27.2 D1 11 17 16 1415 PackageD2 121015 19 11 design D3 23 20 18 17 Miss D4 27 33 22 26 28 Total 354...
The following ANOVA model is for a multiple regression model with two independent variables: Degrees of Sum of Mean Source Freedom Squares ...
The following ANOVA model is for a multiple regression model
with two independent variables:
Degrees
of
Sum
of
Mean
Source
Freedom
Squares
Squares
F
Regression
2
60
Error
18
120
Total
20
180
Determine the Regression Mean Square (MSR):
Determine the Mean Square Error (MSE):
Compute the overall Fstat test statistic.
Is the Fstat significant at the 0.05 level?
A linear regression was run on auto sales relative to consumer
income. The Regression Sum of Squares (SSR) was 360 and...
Problem 2. Consider the one-way layout ANOVA model, where we assume that Yij = μί-cij,に1, . . . , I and J 1, . . . ,J, where μί's are fixed unknown with zero mean treatment means and eiy's are random errors , al such that Σ-lai -0 and E[Yj-μ + ai,1- Show that there exists unique numbers μ, ai, a. b. Show that the null hypothesis Ho : μ,-...- μι is equivalent to Ho : 01 ,-. . .-a1-0...
Problem 2. Consider the one-way layout ANOVA model, where we assume that Yij = μί-cij,に1, . . . , I and J 1, . . . ,J, where μί's are fixed unknown with zero mean treatment means and eiy's are random errors , al such that Σ-lai -0 and E[Yj-μ + ai,1- Show that there exists unique numbers μ, ai, a. b. Show that the null hypothesis Ho : μ,-...- μι is equivalent to Ho : 01 ,-. . .-a1-0
(1 point) In order to compare the means of two populations, independent random samples of 271 observations are selected from each population, with the following results: Sample 1 Sample 2 1145 2 120 (a) Use a 99 % confidence interval to estimate the difference between the population means (A-μ). (b) Test the null hypothesis: HO : (μί-12-0 versus the alternative hypothesis. Ha : (μ-μ2)メ (i) the test statistic z () the positive critical z score (ii) the negative critical z...
Question. Consider a random sample X11-X12. . . . , Xini with ni-10 from N2(μ, Σ) and a random sample X21 . X22, . . . , x2n2 with n2 10 from M2(μ2. Σ ), where μί-μί, μί21.- 1,2. The summary statistics of the two samples as follows: 10 -5 s, 10-5 and S2-5 4 1. Test the hypothesis Ho : μ,-,12 versus Hi : μί ,< μ2 at 5% significance level. Hint: Use m1 n2 where Spooled = (n-1)sit2-2...
(1 point) (Give answers to at least two decimal places. For simplicity, use the standard normal distribution bacause the samples are both large.) In order to compare the means of two populations, independent random samples of 4 observations are selected from each population, with the following results: Sample 1 Sample 2 81 -15582-125 Use a 97 % confidence interval to estimate the difference between the population means (M1-12). -304.502 (b) Test the null hypothesis: H0 the test statistic z The...
(1 point) (Give answers to at least two decimal places. For simplicity, use the standard normal distribution bacause the samples are both large.) In order to compare the means of two populations, independent random samples of 93 observations are selected from each population, with the following results: Sample 1 Sample 2 s1 = 170 s2 = 195 (a) Use a 98 % confidence interval to estimate the difference between the population means ( ) - Test the null hypothesis: Ho...
Suppose that X ~ POI(μ), where μ > 0. You will need to use the following fact: when μ is not too close to 0, VR ape x N(VF,1/4). (a) Suppose that we wish to test Ho : μ-710 against Ha : μ μί are given and 10 < μι. m, where 140 and Using 2 (Vx-VHo) as the test statistic, find a critical region (rejection region) with level approximately a (b) Now suppose that we wish to test Ho...
Why do we need time n when we calculate SSTR? In other words,
why n times (mean of a factor level - mean of
total)^2 Could you give me some intuitive explanation or
proof?
Here are my lecture notes.
Store IDs Total Mean ni S1 S2 S3 S4 S5(Y) 73 67 78 136 14.6 13.4 19.5 27.2 D1 11 17 16 1415 PackageD2 121015 19 11 design D3 23 20 18 17 Miss D4 27 33 22 26 28 Total 354...
The following ANOVA model is for a multiple regression model
with two independent variables:
Degrees
of
Sum
of
Mean
Source
Freedom
Squares
Squares
F
Regression
2
60
Error
18
120
Total
20
180
Determine the Regression Mean Square (MSR):
Determine the Mean Square Error (MSE):
Compute the overall Fstat test statistic.
Is the Fstat significant at the 0.05 level?
A linear regression was run on auto sales relative to consumer
income. The Regression Sum of Squares (SSR) was 360 and...
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