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The quantity of dissolved exygen is a measure of water polution in lakes, ivers, and streams. Water samples were taken at four different locations in a river in an effort to determineater poluon varied from location to location. Location I was 500 meters above an industrial plant water discharge point and near the shore. Location I1 was 200 meters above the discharge point and in midstream. Location 1l was 5 meters downstream from the discharge point and near the shore. Location V was 200 meters downstream from the discharge point and in midstream. The following table shows the results. Lower dissolved oxygen readings mean more polution. Because of the dificuty in getting midstream samples, ecology students collecting the data had fewer of these samples. Use a 10% level of significance. Do we reject or not reject the daim that the quantity ef dissolved exygen dees not vary frem one lecation to another Location I Location II Lecation I Location IV 4.7 5.6 OWhat is the level of signifcance State the nul and alternate hypotheses OH ai N All four means are diferent. OH ai Exactly three means are equal. OMI H i MNot all the means are equal OMI MExactly two means are equa () Find SSor Sarn and sS and check that SSor Ssr SS (Use 3 decimal places.) SSar Find den d MSen and MS (Use 3 decimal places for MSen and MS - Find the value of the sample F statistic. (Use 3 decimal places.) what are the degrees or (nhumerator) |(denominator) () Find the Pvalue of the sample test statistic. Use 4decimal places.) O 4) Based on y canen in parts (a) te (eh w

The quantity of dissolved exygen is a measure of water polution in lakes, ivers, and streams. Water samples were taken at four different locations in a river in an effort to determineater poluon varied from location to location. Location I was 500 meters above an industrial plant water discharge point and near the shore. Location I1 was 200 meters above the discharge point and in midstream. Location 1l was 5 meters downstream from the discharge point and near the shore. Location V was 200 meters downstream from the discharge point and in midstream. The following table shows the results. Lower dissolved oxygen readings mean more polution. Because of the dificuty in getting midstream samples, ecology students collecting the data had fewer of these samples. Use a 10% level of significance. Do we reject or not reject the daim that the quantity ef dissolved exygen dees not vary frem one lecation to another Location I Location II Lecation I Location IV 4.7 5.6 OWhat is the level of signifcance State the nul and alternate hypotheses OH ai N All four means are diferent. OH ai Exactly three means are equal. OMI H i MNot all the means are equal OMI MExactly two means are equa () Find SSor Sarn and sS and check that SSor Ssr SS (Use 3 decimal places.) SSar Find den d MSen and MS (Use 3 decimal places for MSen and MS - Find the value of the sample F statistic. (Use 3 decimal places.) what are the degrees or (nhumerator) |(denominator) () Find the Pvalue of the sample test statistic. Use 4decimal places.) O 4) Based on y canen in parts (a) te (eh w

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The quantity of dissolved oxygen is a measure of water pollution in lakes, rivers, and streams. Water samples were taken at four different locations in a river in an effort to determine if water pollution varied from location to location. Location I was 500 meters above an industrial plant water discharge point and near the shore. Location II was 200 meters above the discharge point and in midstream. Location III was 50 meters downstream from the discharge point and near the shore. Location IV was 200 meters downstream from the discharge point and in midstream. The following table shows the results. Lower dissolved oxygen readings mean more pollution. Because of the difficulty in getting midstream samples, ecology students collecting the data had fewer of these samples. Use a 10% level of significance. Do we reject or not reject the claim that the quantity of dissolved oxygen does not vary from one location to another? Location I Location II Location III Location IV 7.1 6.6 4.3 4.7 6.7 7.3 5.5 5.6 7.5 7.9 4.6 6.7 6.7 7.8 5.5 6.2 4.3 (a) What is the level of significance? State the null and alternate hypotheses. O H,: H1 = H, = H3 = Ha; H,: All four means are different. O H,: H1 = H2 = H3 = H4i H;: Exactly three means are equal. O H,: H1 = H2 = H3 = Ha; H,: Not all the means are equal. O H.: H1 = H2 = H3 = Hại H: Exactly two means are equal. (b) Find SSTOT, SSBET, and Sw and check that SSTOT = SSBET + Ssw. (Use 3 decimal places.) SSTOT= SSBET=L SSw=l Find d.f. BET, d.f. w, MSBET, and MSw. (Use 3 decimal places for MSBET, and MSw:) dfBET = dfw = MS BET= MSw= Find the value of the sample F statistic. (Use 3 decimal places.) What are the degrees of freedom? (numerator) (denominator) (c) Find the P-value of the sample test statistic. (Use 4 decimal places.) (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? O Since the P value is greater than the level of significance at a = 0.1, we do not reject Ho: O Since the P value is less than or equal to the level of significance at a = 0.1, we reject Ho: O Since the P value is greater than the level of significance at a = 0.1, we reject Ho. O Since the P value is less than or equal to the level of significance at a = 0.1, we do not reject Ho: (e) Interpret your conclusion in the context of the application. O At the 10% level of significance there is insufficient evidence to conclude that the means are not all equal. O At the 10% level of significance there is sufficient evidence to conclude that the means are not all equal. O At the 10% level of significance there is insufficient evidence to conclude that the means are all equal. O At the 10% level of significance there is sufficient evidence to conclude that the means are all equal. (f) Make a summary table for your ANOVA test. Source of Degrees of Freedom Sum of F Test MS P Value Variation Squares Ratio Decision Between groups ---Select--- Within groups Total
Transcribed Image Text:The quantity of dissolved oxygen is a measure of water pollution in lakes, rivers, and streams. Water samples were taken at four different locations in a river in an effort to determine if water pollution varied from location to location. Location I was 500 meters above an industrial plant water discharge point and near the shore. Location II was 200 meters above the discharge point and in midstream. Location III was 50 meters downstream from the discharge point and near the shore. Location IV was 200 meters downstream from the discharge point and in midstream. The following table shows the results. Lower dissolved oxygen readings mean more pollution. Because of the difficulty in getting midstream samples, ecology students collecting the data had fewer of these samples. Use a 10% level of significance. Do we reject or not reject the claim that the quantity of dissolved oxygen does not vary from one location to another? Location I Location II Location III Location IV 7.1 6.6 4.3 4.7 6.7 7.3 5.5 5.6 7.5 7.9 4.6 6.7 6.7 7.8 5.5 6.2 4.3 (a) What is the level of significance? State the null and alternate hypotheses. O H,: H1 = H, = H3 = Ha; H,: All four means are different. O H,: H1 = H2 = H3 = H4i H;: Exactly three means are equal. O H,: H1 = H2 = H3 = Ha; H,: Not all the means are equal. O H.: H1 = H2 = H3 = Hại H: Exactly two means are equal. (b) Find SSTOT, SSBET, and Sw and check that SSTOT = SSBET + Ssw. (Use 3 decimal places.) SSTOT= SSBET=L SSw=l Find d.f. BET, d.f. w, MSBET, and MSw. (Use 3 decimal places for MSBET, and MSw:) dfBET = dfw = MS BET= MSw= Find the value of the sample F statistic. (Use 3 decimal places.) What are the degrees of freedom? (numerator) (denominator) (c) Find the P-value of the sample test statistic. (Use 4 decimal places.) (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? O Since the P value is greater than the level of significance at a = 0.1, we do not reject Ho: O Since the P value is less than or equal to the level of significance at a = 0.1, we reject Ho: O Since the P value is greater than the level of significance at a = 0.1, we reject Ho. O Since the P value is less than or equal to the level of significance at a = 0.1, we do not reject Ho: (e) Interpret your conclusion in the context of the application. O At the 10% level of significance there is insufficient evidence to conclude that the means are not all equal. O At the 10% level of significance there is sufficient evidence to conclude that the means are not all equal. O At the 10% level of significance there is insufficient evidence to conclude that the means are all equal. O At the 10% level of significance there is sufficient evidence to conclude that the means are all equal. (f) Make a summary table for your ANOVA test. Source of Degrees of Freedom Sum of F Test MS P Value Variation Squares Ratio Decision Between groups ---Select--- Within groups Total
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