Two college instructors are interested in whether or not there is any variation in the way they grade math exams. They each grade the same set of 10 exams. The first instructor's grades have a variance of 41.59. The second instructor's grades have a variance of 65.44. What is the Test Statistic to test the Null Hypothesis H0: σ12 ≥ σ22 against the alternative Ha: σ12 < σ2 2 ?

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ou may need to use the appropriate technology to answer this question. The following data are from a completely randomized design. In the following calculations, use  ? = 0.05.   Treatment1 Treatment2 Treatment3   62 82 70 46 71 53 53 87 60 39 64 45 xj 50 76 57 sj2 96.67 108.67 112.67 (a) Use analysis of variance to test for a significant difference among the means of the three treatments. State the null and alternative hypotheses. H0: ?1 ≠ ?2 ≠ ?3Ha: ?1 = ?2 = ?3H0: ?1 = ?2 = ?3Ha: Not all the population means are equal.    H0: Not all the population means are equal.Ha: ?1 = ?2 = ?3H0: ?1 = ?2 = ?3Ha: ?1 ≠ ?2 ≠ ?3H0: At least two of the population means are equal.Ha: At least two of the population means are different. Find the value of the test statistic. (Round your answer to two decimal places.)   Find the p-value. (Round your answer to three decimal places.) p-value =  State your conclusion. Do not reject H0. There is sufficient evidence to conclude that…

Consider the experimental results for the following randomized block design. Make the calculations necessary to set up the analysis of variance table.     TREATMENTS             A B C     Blocks 1 11 9 8       2 12 6 5       3 18 15 14       4 20 18 18       5 8 7 8     Use ? = 0.05 to test for any significant differences. State the null and alternative hypotheses. -H0: Not all the population means are equal.Ha: ?A = ?B = ?C -H0: ?A = ?B = ?C- Ha: Not all the population means are equal.     -H0: ?A = ?B = ?CHa: ?A ≠ ?B ≠ ?C -H0: At least two of the population means are equal.Ha: At least two of the population means are different. -H0: ?A ≠ ?B ≠ ?CHa: ?A = ?B = ?C Find the value of the test statistic. (Round your answer to two decimal places.) Test statistic=?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? State your conclusion. -Reject H0. There is sufficient evidence to conclude that the means of the three treatments are not equal…

Which outcome is expected if the null hypothesis is true for an analysis of variance? a. SSbetween should be about the same size as SStotal.​ ​b. SSbetween should be about the same size as SSwithin. ​c. MSbetween should be about the same size as MStotal. ​d. MSbetween should be about the same size as MSwithin.

A transect is an archaeological study area that is 1/5 mile wide and 1 mile long. A site in a transect is the location of a significant archaeological find. Let x represent the number of sites per transect. In a section of Chaco Canyon, a large number of transects showed that x has a population variance ?2 = 42.3. In a different section of Chaco Canyon, a random sample of 19 transects gave a sample variance s2 = 46.9 for the number of sites per transect. Use a 5% level of significance to test the claim that the variance in the new section is greater than 42.3. Find a 95% confidence interval for the population variance. (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)- 19.96 What are the degrees of freedom? -18 (c) Find or estimate 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 < 0.0250.005 < P-value < 0.010P-value < 0.005…

A transect is an archaeological study area that is 1/5 mile wide and 1 mile long. A site in a transect is the location of a significant archaeological find. Let x represent the number of sites per transect. In a section of Chaco Canyon, a large number of transects showed that x has a population variance ?2 = 42.3. In a different section of Chaco Canyon, a random sample of 21 transects gave a sample variance s2 = 49.3 for the number of sites per transect. Use a 5% level of significance to test the claim that the variance in the new section is greater than 42.3................

Two separate samples, each with 16 individuals, receive two different treatments. After treatment, the first sample has SS = 1540 and the second has SS = 1460. a. Find the pooled variance, s2p, for the two samples b. The estimated standard error is c. If the sample mean difference is 10 points (i.e., M1 -  M2 = 10), compute the t-statistic. The t-statistic is:

As a marketing class term project, Jim is investigating whether senior students eat less frequently in fast-food chains than college freshmen. He asked 11 freshmen and 11 seniors to keep track of how many times they ate in a fast-food restaurant during the month of November. Assuming equal variances unknown, do a left-tailed test of Hypothesis whether he conclude that the mean is significantly smaller for college seniors than freshmen at the 5% level of significance. [Freshmen(F) -> 11 18 12 7 16 20 15 14 17 9 16 Senior(S) => 5 13 15 5 10 8 9 8 19 7 18 a) Carry out the hypothesis test above and draw the conclusion of the test, where S-mean = 10.64, F-mean = 14.09, S-variance = 24.25, F-variance = 15.69 b) What is the p-value for left-tailed test in a) -> used by z table (use up to 2nd decimal point value of tr, in a).