There 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 69 28 15 30 17 35 24 53 65 10 68 20 77 17 57 15 26 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. (a) What is the level of significance?State the null and alternate hypotheses. H0: μ1 = μ2 = μ3; H1: Not all the means are equal.H0: μ1 = μ2 = μ3; H1: At least two means are equal. H0: μ1 = μ2 = μ3; H1: Exactly two means are equal.H0: μ1 = μ2 = μ3; H1: All three means are different. (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

There 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 69 28 15 30 17 35 24 53 65 10 68 20 77 17 57 15 26 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. (a) What is the level of significance?State the null and alternate hypotheses. H0: μ1 = μ2 = μ3; H1: Not all the means are equal.H0: μ1 = μ2 = μ3; H1: At least two means are equal. H0: μ1 = μ2 = μ3; H1: Exactly two means are equal.H0: μ1 = μ2 = μ3; H1: All three means are different. (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

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Description: There 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,

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 34PPS

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Site I	Site II	Site III
69	28	15
30	17	35
24	53	65
10	68	20
77		17
57		15
26

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.

(a) What is the level of significance?

State the null and alternate hypotheses.

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

(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

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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