T test statistic
Conduct a test of hypothesis that the mean mileage of makes 2 and 3 do not differ. Use the method for single means when σ is not known with the Error MS serving as the pooled variance Reminders: Test statistic t- difference of means / standard error of difference of means. The standard error of the difference equals square root of the sum of variances of the two means. The variance of each mean is estimated by the error mean square/number of observations in that mean 13. What is the value of the t test statistic for testing the hypothesis that makes 2 and 3 do not differ in mileage'? Example 24
Homework Answers
Sp^2 = (10.15873 + 13.06164)/2 = 11.610185
t = (Xbar 2 - Xbar3)/(sqrt( Sp^2 (1/n2 + 1/n3))
= ( 10.85455-21.91818 ) / sqrt(11.610185 * (1/11 + 1/11 ))
= - 7.6148
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Anova: Single Factor SUMMARY Groups Count CAR1 CAR2 CAR3 CAR4 SumAverage Variance 178.9 19.87778 ...
Question Completion Status QUESTION 4 Anova: Single Factor SUMMARY Groups Count Sum Average Variance A 4...
Question Completion Status QUESTION 4 Anova: Single Factor SUMMARY Groups Count Sum Average Variance A 4 108 27 32.66666667 B 4 96 24 13.33333333 4 120 30 56 ANOVA Source of Variation SS df F crit MS P-value F Treatments 72 36 1.058823529 0.386396621 4.256494729 Error 306 9 34 Total 378 11 Based on the Results above of Single Factor ANOVA: the MSTR O 36 O 378 O 72 O 34 Click Save and Submit to save and submit. Chick...
Anova: Single Factor SUMMARY Groups Count Average Variance A 30 4.967 5.344 B 30 4.567 3.220...
Anova: Single Factor SUMMARY Groups Count Average Variance A 30 4.967 5.344 B 30 4.567 3.220 C 30 7.267 7.375 D 30 6.500 7.638 E 30 9.400 12.248 Compare Group E to Group A What is the t-value for this test? What is the P-value for this test? What is the confidence interval for mean difference in this test? Keeping in mind that the Margin of Error is the difference from the mean difference to either value above, what is...
Anova: Two-Factor With Replication SUMMARY Fitness1 Fitness2 Fitness3 Total Age 40 Count Sum Aver...
Anova: Two-Factor With Replication SUMMARY Fitness1 Fitness2 Fitness3 Total Age 40 Count Sum Average Variance 27612.5 29621.78544.5 30818.88 848.81058.6 1459.6 424.4529.3 729.8 561.1667 3367 Age 50 Count Sum Average Variance 11130.32 15931.13 48329.41 81373.3 5991332.3 1734.5 3665.8 2995666.15 867.25 610.9667 Age 60 Count Sum Average 826.65989.91282.1 1032.883 Variance 52715.05 2164.82 73497.78 68271.01 2 1653.3 1979.8 2564.26197.3 Total Count Sum Average516.85728.45 959.7167 Variance 78997.254302.79 90611.45 3101.14370.75758.3 ANOVA Source of Varid SS MS P-value F crit Sample806020.7 Columns 588779.4 Interactio 51989.25 Within...
(Harder question): Show that the two sample t-test statistic squared is equal to the single-factor ANOVA...
(Harder question): Show that the two sample t-test statistic squared is equal to the single-factor ANOVA F statistic when there are two levels. For simplicity, assume equal sample size of n in each of the two groups RECALL: Two sided, two independent sample pooled t-test tests the following hypotheses: The test statistic is: VEA where yi and ỹ2 are the sample means in group 1 and 2, respectively. The pooled variance is given by where s and s3 are the...
In ANOVA, variability between groups reflects _________, whereas variability within groups reflects __________ . total variance;...
In ANOVA, variability between groups reflects _________, whereas variability within groups reflects __________ . total variance; error variance error variance ; total variance random error; a true effect (if one exists) both a true effect (if one exists) and random error; only random error just a true effect (if one exists); random error Rejecting the null hypothesis with the overall or omnibus One-way Analysis of Variance indicates that the: mean of one sample differs significantly from the mean of at...
Anova: Single Factor SUMMARY Count Av Variance Sum 165.000000000 27.500000000 8.300000000 174.000000000 29.000000000 2.000000000 155.000000000 25.833333333...
Anova: Single Factor SUMMARY Count Av Variance Sum 165.000000000 27.500000000 8.300000000 174.000000000 29.000000000 2.000000000 155.000000000 25.833333333 1.366666667 188.000000000 31.333333333 0.666666667 ANOVA P.value Fcrit Between Groups 98.166666667 3 Within Groups 61.666666667 20 MS 32.722222222 10.612612613 0.000217836 3.098391196 3.083333333 Total 159.833333333 23 TUKEY MULTIPLE COMPARISON TEST Distance 2.838767338 3.96 0.05 Means joined by a double line are not significantly different. 25.833333969 27.500000000 29.000000000 31.333333969 19. Is there a statistically significant difference in the average processing time between the four products? A. Yes,...
ITs a stats problem Note that the analysis of variance F test for testing for treatment...
ITs a stats problem
Note that the analysis of variance F test for testing for treatment effects in a CRD with p- 2 treatments is equivalent to testing for equality of treatment means in the pooled two-sample t-test. Recall that the pooled two-sample t test statistic is given by (ni-1)sỈ + (n2-1)s n n2-2 where s2- 2, 2-i is the sample mean of the ith treatment group, s? is the sample variance of the ih treatment group, and n, is...
3. (Harder question): Show that the two sample t-test statistic squared is equal to the single-factor...
3. (Harder question): Show that the two sample t-test statistic squared is equal to the single-factor ANOVA F statistic when there are two levels. For simplicity, assume equal sample size of n in each of the two groups RECALL : Two sided, two independent sample pooled t-test tests the following hypotheses: The test statistic is: - y2 where and 2 are the sample means in group 1 and 2, respectively. The pooled variance is given by (w, where s and...
3. (Harder question): Show that the two sample t-test statistic squared is equal to the single-factor...
3. (Harder question): Show that the two sample t-test statistic squared is equal to the single-factor ANOVA F statistic when there are two levels. For simplicity, assume equal sample size of n in each of the two groups RECALL: Two sided, two independent sample pooled t-test tests the following hypotheses: The test statistic is: 1-y2 where i and 2 are the sample means in group 1 and 2, respectively. The pooled variance is given by where s and s3 are...
3. (Harder question): Show that the two sample t-test statistic squared is equal to the single-factor...
3. (Harder question): Show that the two sample t-test statistic squared is equal to the single-factor ANOVA F statistic when there are two levels. For simplicity, assume equal sample size of n in each of the two groups. RECALL: Two sided, two independent sample pooled t-test tests the following hypotheses: The test statistic is: y2 where yi and 2 are the sample means in group 1 and 2, respectively. The pooled variance is given by 2 where s and s...
Question Completion Status QUESTION 4 Anova: Single Factor SUMMARY Groups Count Sum Average Variance A 4 108 27 32.66666667 B 4 96 24 13.33333333 4 120 30 56 ANOVA Source of Variation SS df F crit MS P-value F Treatments 72 36 1.058823529 0.386396621 4.256494729 Error 306 9 34 Total 378 11 Based on the Results above of Single Factor ANOVA: the MSTR O 36 O 378 O 72 O 34 Click Save and Submit to save and submit. Chick...
Anova: Two-Factor With Replication SUMMARY Fitness1 Fitness2 Fitness3 Total Age 40 Count Sum Average Variance 27612.5 29621.78544.5 30818.88 848.81058.6 1459.6 424.4529.3 729.8 561.1667 3367 Age 50 Count Sum Average Variance 11130.32 15931.13 48329.41 81373.3 5991332.3 1734.5 3665.8 2995666.15 867.25 610.9667 Age 60 Count Sum Average 826.65989.91282.1 1032.883 Variance 52715.05 2164.82 73497.78 68271.01 2 1653.3 1979.8 2564.26197.3 Total Count Sum Average516.85728.45 959.7167 Variance 78997.254302.79 90611.45 3101.14370.75758.3 ANOVA Source of Varid SS MS P-value F crit Sample806020.7 Columns 588779.4 Interactio 51989.25 Within...
(Harder question): Show that the two sample t-test statistic squared is equal to the single-factor ANOVA F statistic when there are two levels. For simplicity, assume equal sample size of n in each of the two groups RECALL: Two sided, two independent sample pooled t-test tests the following hypotheses: The test statistic is: VEA where yi and ỹ2 are the sample means in group 1 and 2, respectively. The pooled variance is given by where s and s3 are the...
Anova: Single Factor SUMMARY Count Av Variance Sum 165.000000000 27.500000000 8.300000000 174.000000000 29.000000000 2.000000000 155.000000000 25.833333333 1.366666667 188.000000000 31.333333333 0.666666667 ANOVA P.value Fcrit Between Groups 98.166666667 3 Within Groups 61.666666667 20 MS 32.722222222 10.612612613 0.000217836 3.098391196 3.083333333 Total 159.833333333 23 TUKEY MULTIPLE COMPARISON TEST Distance 2.838767338 3.96 0.05 Means joined by a double line are not significantly different. 25.833333969 27.500000000 29.000000000 31.333333969 19. Is there a statistically significant difference in the average processing time between the four products? A. Yes,...
ITs a stats problem
Note that the analysis of variance F test for testing for treatment effects in a CRD with p- 2 treatments is equivalent to testing for equality of treatment means in the pooled two-sample t-test. Recall that the pooled two-sample t test statistic is given by (ni-1)sỈ + (n2-1)s n n2-2 where s2- 2, 2-i is the sample mean of the ith treatment group, s? is the sample variance of the ih treatment group, and n, is...
3. (Harder question): Show that the two sample t-test statistic squared is equal to the single-factor ANOVA F statistic when there are two levels. For simplicity, assume equal sample size of n in each of the two groups RECALL : Two sided, two independent sample pooled t-test tests the following hypotheses: The test statistic is: - y2 where and 2 are the sample means in group 1 and 2, respectively. The pooled variance is given by (w, where s and...
3. (Harder question): Show that the two sample t-test statistic squared is equal to the single-factor ANOVA F statistic when there are two levels. For simplicity, assume equal sample size of n in each of the two groups RECALL: Two sided, two independent sample pooled t-test tests the following hypotheses: The test statistic is: 1-y2 where i and 2 are the sample means in group 1 and 2, respectively. The pooled variance is given by where s and s3 are...
3. (Harder question): Show that the two sample t-test statistic squared is equal to the single-factor ANOVA F statistic when there are two levels. For simplicity, assume equal sample size of n in each of the two groups. RECALL: Two sided, two independent sample pooled t-test tests the following hypotheses: The test statistic is: y2 where yi and 2 are the sample means in group 1 and 2, respectively. The pooled variance is given by 2 where s and s...
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