30 43 36 30 44 35 26 46 36 32 48 40 Sample mean 30 45 36 Sample variance 6.00 4.00 6.50
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The following data are from a completely randomized design.
Treatment A
Treatment B
Treatment C
32
44
33
30
43
36
30
44
35
26
46
36
32
48
40
Sample mean
30
45
36
Sample variance
6.00
4.00
6.50
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At the level of significance, can we reject the null hypothesis that the means of the three treatments are equal?
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Use Fisher’s LSD procedure to test whether there is a significant difference between the means for treatments A and B, treatments A and C, and treatments B and C. Use .
-
Use Fisher’s LSD procedure to develop a 95% confidence
interval estimate of the difference between the means of treatments A and B.
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- An experiment was designed to investigate the effect of lighting on egg production of pullets. The experiment consisted of four randomized block of three treatments each. The number of eggs laid by a pen of six pullets were recorded for three months. Blocks Treatments 1 2 3 4 O 330 288 295 313 E 372 340 343 341 F 359 337 373 302 Construct analysis of variance (ANOVA) table and use it to test the hypothesis that atleast a pair of the treatments are significantly different.The following data are from a completely randomized design. TreatmentA TreatmentB TreatmentC 31 45 34 29 42 37 29 44 36 26 45 37 30 49 41 Sample mean 29 45 37 Sample variance 3.50 6.50 6.50 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 = (b) Use Fisher's LSD procedure to test whether there is a significant difference between the means for treatments A and B, treatments A and C, and treatments B and C. Use ? = 0.05. Find the value of LSD. (Round your answer to two decimal places.) LSD = Find the pairwise absolute difference between sample means for each pair of treatments. xA − xB = xA − xC = xB − xC = Which treatment means differ significantly? (Select all that apply.) There is a significant difference between the means for treatments A and B.There is a significant difference between the means…A researcher has used a one-way analysis of variance model to test whether the average starting salaries differ among recent graduates from the nursing, engineering, business, and education disciplines. She has randomly selected four graduates from each of the four areas. If MSE = 4, and SSTO = 120, complete the following ANOVA table. Is there a significant difference in the starting salaries among the four disciplines? (H0: No difference) Source SS DF MS F Treatment Error 4 Total 120
- The following data are from a completely randomized design. In the following calculations, use ? = 0.05. Treatment1 Treatment2 Treatment3 62 83 70 46 71 54 53 88 60 39 70 48 xj 50 78 58 sj2 96.67 79.33 88.00 (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: Not all the population means are equal.H0: ?1 = ?2 = ?3Ha: ?1 ≠ ?2 ≠ ?3 H0: At least two of the population means are equal.Ha: At least two of the population means are different.H0: ?1 ≠ ?2 ≠ ?3Ha: ?1 = ?2 = ?3H0: Not all the population means are equal.Ha: ?1 = ?2 = ?3 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 not sufficient evidence to conclude that the means of the three treatments are not equal.Reject H0. There is…An experiment was conducted to study the life (in hours) of two different brands of batteries in threedifferent devices (radio, camera, and portable DVD player). A completely randomized two-factorexperiment was conducted, and the following data resulted.Brand Deviceof Battery Radio Camera DVD PlayerA 8.6 7.9 5.48.2 8.4 5.7B 9.4 8.5 5.88.8 8.9 5.9(a) Analyze the data and draw conclusions, using α = 0.05. (b) Investigate model adequacy by plotting the residuals. (c) Which brand of batteries would you recommend?The following data were obtained in a study using three separate samples to compare three different treatments. Conduct an analysis of variance (ANOVA) with α=0.05 to determine whether these data are sufficient to conclude that there are significant differences between the treatments. Treatment A Treatment B Treatment C 16 16 17 18 16 19 17 14 21 17 14 19 F-ratio = _______ (3 decimal places)p-value = _________ (3 decimal places) Treatment A Treatment B Treatment C 15 17 16 19 16 19 17 14 22 17 13 19 F-ratio = ________ (3 decimal places)p-value = _________(3 decimal places)
- Consider the following data obtained for two samples selected at random from twopopulations that are independent and normally distributed with equal variances.Sample I Sample II32 2726 3531 3320 4027 3834 31Test at the 1% significance level whether the means of the populations from whichthese samples are drawn are equal.A standardized math test was administered to two groups of 5th graders, one group sampled from classes whose teachers had followed the existing curriculum and one group sampled from classes whose teachers had followed a new curriculum, and the scores were compared using a t-test with the following results: t-test: Two-Sample Assuming Equal Variances Old Curriculum New Curriculum Mean 75.31914894 65.65957447 Variance 118.613321 801.1424607 Obervations 47 47 Hypothesized Mean Difference 0 df 92 t Stat 2.183587807 P(T<=t) one-tail 0.015768226 t Critical one-tail 1.661585397 P(T<=t) two-tail 0.031536452 t Critical two-tail…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…
- The following table shows a partially completed ANOVA hypothesis test using a completely randomized design. Source of Variation SS df MS F Between samples 4 4 Within Samples 56.68 Total 72.11 24 (i) Determine the total number of observations in this ANOVA test. (ii) How many populations are compared in the ANOVA test. (iii) Complete the ANOVA table.The following data summarize the results from an independent-measures study comparing three treatment conditions. I II III n =10 n =10 n =10 s2 = 2.67 s2 = 2.00 s2 = 1.33 M =2 M =3 M =4 T = 20 T = 30 T = 40 Q.3.1. Use an ANOVA with α =.05 to determine whether there are any significant mean differences among the three means. (show your working). Hint: because the samples are all the same size, MSwihin is the average of the three sample variances.Independent random samples of 32 people living on the west side of a city and 30 people living on the east side of a city were taken to determine if the income levels of west side residents are significantly different from the income levels of east side residents. Given the testing statistics below, determine if the data provides sufficient evidence to conclude that the income levels of west side residents are significantly different from the income levels of east side residents, at the 2% significance level. H0:μw=μeHa:μw≠μe t0=2.364 t0.01=±2.099 Select the correct answer below: No; the test statistic is not between the critical values. No; the test statistic is between the critical values. Yes; the test statistic is not between the critical values. Yes; the test statistic is between the critical values.