Listed below are time intervals (min) between eruptions of a geyser. The "recent" times are within the pastfew years, and the "past" times are from 1995. Does it appear that the variation of the times betweeneruptions has changed? Use a 0.05 significance level. Assume that the two populations are normallydistributed.Click the icon to view the sample data.The P-value is(Round to three decimal places as needed.)What is the conclusion for this hypothesis test?O A. Reject Ho There is sufficient evidence to support the claim that the variation of the timesbetween eruptions has changed.O B. Reject Ho There is insufficient evidence to support the claim that the variation of the timesbetween eruptions has changed.O C. Fail to reject H,. There is sufficient evidence to support the claim that the variation of thetimes between eruptions has changed.O D. Fail to reject H,. There is insufficient evidence to support the claim that the variation of theClick to select your answer(s). Listed below are time intervals (min) between eruptions of a geyser. The "recent" times are within the past few years, and the "past" times are from 1995. Does it appear that the variation of the times between eruptions has changed?Use a 0.05 significance level. Assume that the two populations are normally distributed.E Click the icon to view the sample data.- XSample dataIdentify the test statistic.The test statistic is(Round to two decimal places as needed.)Identify the P-valueRecent799589755597669066868187Past9285 9499 6882 899884989291The P-value is(Round to three decimal places as needed.)PrintDoneWhat is the conclusion for this hypothesis test?O A. Reject Ho. There is sufficient evidence to support the claim that the variation of the times between eruptions has changed.O B. Reject Ho. There is insufficient evidence to support the claim that the variation of the times between eruptions has changed.OC. Fail to reject Hg. There is sufficient evidence to support the claim that the variation of the times between eruptions has changed.O D. Fail to reject H There is insufficient evidence to support the claim that the variation of the times between eruptions has changed

Name: Listed below are time intervals (min) between eruptions of a geyser.
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Description: Listed below are time intervals (min) between eruptions of a geyser. The "recent" times are within the pastfew years, and the "past" times are from 1995. Does it appear that the variation of the times betweeneruptions has changed? Use a 0.05 signifi

The following table is obtained: Group 1 (Recent) Group 2 (Past) 79 92 95 85 89 94 75 99 55 68 97 82 66 89 90 98 66 84 86 98 81 92 87 91 Sum = 966 1072 Average = 80.5 89.333 ∑iXij2=\sum_i X_{ij}^2 = 79584 96604 St. Dev. = 12.866 8.732 SS = 1821 838.666 n = 12 12 The total sample size is N=24N = 24. Therefore, the total degrees of freedom are: dftotal=24−1=23df_{total} = 24 - 1 = 23 Also, the between-groups degrees of freedom are dfbetween=2−1=1df_{between} = 2 - 1 = 1, and the within-groups degrees of freedom are: dfwithin=dftotal−dfbetween=23−1=22df_{within} = df_{total} - df_{between} = 23 - 1 = 22 First, we need to compute the total sum of values and the grand mean. The following is obtained ∑i,jXij=966+1072=2038\sum_{i,j} X_{ij} = 966+1072 = 2038i Also, the sum of squared values is ∑i,jXij2=79584+96604=176188\sum_{i,j} X_{ij}^2 = 79584+96604 = 176188 Based on the above calculations, the total sum of squares is computed as follows SStotal=∑i,jXij2−1N(∑i,jXij)2=176188−2038224=3127.833SS_{total} = \sum_{i,j} X_{ij}^2 - \frac{1}{N} \left(\sum_{i,j} X_{ij}\right)^2 = 176188 - \frac{ 2038^2}{ 24} = 3127.833 The within sum of squares is computed as shown in the calculation below: SSwithin=∑SSwithingroups=1821+838.66666666667=2659.667SS_{within} = \sum SS_{within groups} = 1821+838.66666666667 = 2659.667 The between sum of squares is computed directly as shown in the calculation below: Now that sum of squares are computed, we can proceed with computing the mean sum of squares: MSbetween=SSbetweendfbetween=468.1671=468.167MS_{between} = \frac{SS_{between}}{df_{between}} = \frac{ 468.167}{ 1} = 468.167 MSwithin=SSwithindfwithin=2659.66722=120.894MS_{within} = \frac{SS_{within}}{df_{within}} = \frac{ 2659.667}{ 22} = 120.894 Now that sum of squares are computed, we can proceed with computing the mean sum of squares: MSbetween=SSbetweendfbetween=468.1671=468.167MS_{between} = \frac{SS_{between}}{df_{between}} = \frac{ 468.167}{ 1} = 468.167 MSwithin=SSwithindfwithin=2659.66722=120.894MS_{within} = \frac{SS_{within}}{df_{within}} = \frac{ 2659.667}{ 22} = 120.894 Finally, with having already calculated the mean sum of squares, the F-statistic is computed as follows: F=MSbetweenMSwithin=468.167120.894=3.873F = \frac{MS_{between}}{MS_{within}} = \frac{ 468.167}{ 120.894} = 3.873 Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: μ1 = μ2 (all 2 population means are equal) Ha: Not all means are equal The above hypotheses will be tested using an F-ratio for a One-Way ANOVA. Rejection Region Based on the information provided, the significance level is α=0.05\alpha = 0.05, and the degrees of freedom are df1=1df_1 = 1and df2=1 , therefore, the rejection region for this F-test is R={F:F>Fc=4.301}. Test Statistics F=MSbetweenMSwithin=468.167120.894=3.873F = \frac{MS_{between}}{MS_{within}} = \frac{ 468.167}{ 120.894} = 3.873 Decision about the null hypothesis Since it is observed that F=3.873≤Fc=4.301F = 3.873 \leq F_c = 4.301, it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value is p=0.0618p = 0.0618, and since p=0.0618≥0.05p = 0.0618 \geq 0.05, it is concluded that the null hypothesis is not rejected. Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that not all 2 population means are equal, at the α=0.05\alpha = 0.05. Option D , There is insufficient evidence to support claim that the variation of the times between eruption has changed

Math

Statistics

O Sample data Identify the test statistic The test statistic is (Round to two decimal places as needed) Identify the P-value Recent 79 95 89 75 55 97 66 90 66 86 81 87 Past 92 85 94 99 68 82 89 98 84 98 92 91 The P-value is (Round to three decimal places as needed) Print Done What is the conclusion for this hypothesis test? O A. Reject Ha. There is sufficient evidence to support the claim that the variation of the times between eruptions has changed. O B. Reject H. There is insufficient evidence to support the claim that the variation of the times between eruptions has changed OC. Fail to reject Hg There is sufficient evidence to support the claim that the variation of the times between eruptions has changed. OD. Fail to reject Hg There is insufficient evidence to support the claim that the variation of the times between eruptions has changed

O Sample data Identify the test statistic The test statistic is (Round to two decimal places as needed) Identify the P-value Recent 79 95 89 75 55 97 66 90 66 86 81 87 Past 92 85 94 99 68 82 89 98 84 98 92 91 The P-value is (Round to three decimal places as needed) Print Done What is the conclusion for this hypothesis test? O A. Reject Ha. There is sufficient evidence to support the claim that the variation of the times between eruptions has changed. O B. Reject H. There is insufficient evidence to support the claim that the variation of the times between eruptions has changed OC. Fail to reject Hg There is sufficient evidence to support the claim that the variation of the times between eruptions has changed. OD. Fail to reject Hg There is insufficient evidence to support the claim that the variation of the times between eruptions has changed

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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