ere is an archaeological study area located in southwestern New Mexico. Potsherds are broken pieces of prehistoric Native American clay vessels. One type of painted ceramic vessel is called Mimbres classic black-on-white. At three different sites, the number of such sherds was counted in local dwelling excavations. Site I Site II Site III 62 26 11 30 17 31 26 52 68 17 68 26 82 12 52 13 21 Shall we reject or not reject the claim that there is no difference in population mean Mimbres classic black-on-white sherd counts for the three sites? Use a 1% level of significance. State the null and alternate hypotheses. H0: μ1 = μ2 = μ3; H1: All three means are different.H0: μ1 = μ2 = μ3; H1: At least two means are equal. H0: μ1 = μ2 = μ3; H1: Not all the means are equal.H0: μ1 = μ2 = μ3; H1: Exactly two means are equal. (b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Round your answers to three decimal places.) SSTOT = SSBET = SSW = Find d.f.BET, d.f.W, MSBET, and MSW. (Round your answers for MSBET, and MSW to two decimal places.) d.f.BET = d.f.W = MSBET = MSW = Find the value of the sample F statistic. (Round your answer to two decimal places.)What are the degrees of freedom? d.f.N = d.f.D = (c) Find the P-value of the sample test statistic. P-value > 0.1000.050 < P-value < 0.100 0.025 < P-value < 0.0500.010 < P-value < 0.0250.001 < P-value < 0.010P-value < 0.001 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Since the P-value is greater than the level of significance at α = 0.01, we do not reject H0.Since the P-value is less than or equal to the level of significance at α = 0.01, we reject H0. Since the P-value is greater than the level of significance at α = 0.01, we reject H0.Since the P-value is less than or equal to the level of significance at α = 0.01, we do not reject H0. (e) Interpret your conclusion in the context of the application. At the 1% level of significance there is insufficient evidence to conclude that the means are not all equal.At the 1% level of significance there is sufficient evidence to conclude that the means are all equal. At the 1% level of significance there is insufficient evidence to conclude that the means are all equal.At the 1% level of significance there is sufficient evidence to conclude that the means are not all equal. (f) Make a summary table for your ANOVA test. (Round your answers for SS to three decimal places, your MS and F Ratio to two decimal places, and your P-value to four decimal places.) Source ofVariation Sum ofSquares Degrees ofFreedom MS FRatio P-Value TestDecision Between groups ---Select--- p-value > 0.100 0.050 < p-value < 0.100 0.025 < p-value < 0.050 0.010 < p-value < 0.025 0.001 < p-value < 0.010 p-value < 0.001 ---Select--- Reject H0. Do not reject H0. Within groups Total

ere is an archaeological study area located in southwestern New Mexico. Potsherds are broken pieces of prehistoric Native American clay vessels. One type of painted ceramic vessel is called Mimbres classic black-on-white. At three different sites, the number of such sherds was counted in local dwelling excavations. Site I Site II Site III 62 26 11 30 17 31 26 52 68 17 68 26 82 12 52 13 21 Shall we reject or not reject the claim that there is no difference in population mean Mimbres classic black-on-white sherd counts for the three sites? Use a 1% level of significance. State the null and alternate hypotheses. H0: μ1 = μ2 = μ3; H1: All three means are different.H0: μ1 = μ2 = μ3; H1: At least two means are equal. H0: μ1 = μ2 = μ3; H1: Not all the means are equal.H0: μ1 = μ2 = μ3; H1: Exactly two means are equal. (b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Round your answers to three decimal places.) SSTOT = SSBET = SSW = Find d.f.BET, d.f.W, MSBET, and MSW. (Round your answers for MSBET, and MSW to two decimal places.) d.f.BET = d.f.W = MSBET = MSW = Find the value of the sample F statistic. (Round your answer to two decimal places.)What are the degrees of freedom? d.f.N = d.f.D = (c) Find the P-value of the sample test statistic. P-value > 0.1000.050 < P-value < 0.100 0.025 < P-value < 0.0500.010 < P-value < 0.0250.001 < P-value < 0.010P-value < 0.001 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Since the P-value is greater than the level of significance at α = 0.01, we do not reject H0.Since the P-value is less than or equal to the level of significance at α = 0.01, we reject H0. Since the P-value is greater than the level of significance at α = 0.01, we reject H0.Since the P-value is less than or equal to the level of significance at α = 0.01, we do not reject H0. (e) Interpret your conclusion in the context of the application. At the 1% level of significance there is insufficient evidence to conclude that the means are not all equal.At the 1% level of significance there is sufficient evidence to conclude that the means are all equal. At the 1% level of significance there is insufficient evidence to conclude that the means are all equal.At the 1% level of significance there is sufficient evidence to conclude that the means are not all equal. (f) Make a summary table for your ANOVA test. (Round your answers for SS to three decimal places, your MS and F Ratio to two decimal places, and your P-value to four decimal places.) Source ofVariation Sum ofSquares Degrees ofFreedom MS FRatio P-Value TestDecision Between groups ---Select--- p-value > 0.100 0.050 < p-value < 0.100 0.025 < p-value < 0.050 0.010 < p-value < 0.025 0.001 < p-value < 0.010 p-value < 0.001 ---Select--- Reject H0. Do not reject H0. Within groups Total

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 5E: List the sample space of each experiment. Rolling one die and tossing one coin

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Question

Site I	Site II	Site III
62	26	11
30	17	31
26	52	68
17	68	26
82		12
52		13
21

Shall we reject or not reject the claim that there is no difference in population mean Mimbres classic black-on-white sherd counts for the three sites? Use a 1% level of significance.

State the null and alternate hypotheses.

H₀: μ₁ = μ₂ = μ₃; H₁: All three means are different.H₀: μ₁ = μ₂ = μ₃; H₁: At least two means are equal. H₀: μ₁ = μ₂ = μ₃; H₁: Not all the means are equal.H₀: μ₁ = μ₂ = μ₃; H₁: Exactly two means are equal.

(b) Find SS_TOT, SS_BET, and SS_W and check that SS_TOT = SS_BET + SS_W. (Round your answers to three decimal places.)

SS_TOT	=
SS_BET	=
SS_W	=

Find d.f._BET, d.f._W, MS_BET, and MS_W. (Round your answers for MS_BET, and MS_W to two decimal places.)

d.f._BET	=
d.f._W	=
MS_BET	=
MS_W	=

Find the value of the sample F statistic. (Round your answer to two decimal places.)

What are the degrees of freedom?

d.f._N	=
d.f._D	=

P-value > 0.1000.050 < P-value < 0.100 0.025 < P-value < 0.0500.010 < P-value < 0.0250.001 < P-value < 0.010P-value < 0.001

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Since the P-value is greater than the level of significance at α = 0.01, we do not reject H₀.Since the P-value is less than or equal to the level of significance at α = 0.01, we reject H₀. Since the P-value is greater than the level of significance at α = 0.01, we reject H₀.Since the P-value is less than or equal to the level of significance at α = 0.01, we do not reject H₀.

(e) Interpret your conclusion in the context of the application.

At the 1% level of significance there is insufficient evidence to conclude that the means are not all equal.At the 1% level of significance there is sufficient evidence to conclude that the means are all equal. At the 1% level of significance there is insufficient evidence to conclude that the means are all equal.At the 1% level of significance there is sufficient evidence to conclude that the means are not all equal.

(f) Make a summary table for your ANOVA test. (Round your answers for SS to three decimal places, your MS and F Ratio to two decimal places, and your P-value to four decimal places.)

Source of Variation	Sum of Squares	Degrees of Freedom	MS	F Ratio	P-Value	Test Decision
Between groups					---Select--- p-value > 0.100 0.050 < p-value < 0.100 0.025 < p-value < 0.050 0.010 < p-value < 0.025 0.001 < p-value < 0.010 p-value < 0.001	---Select--- Reject H0. Do not reject H0.
Within groups
Total

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