(a) Calculate n . s for these data, the mean of the variances of the four samples and the value of F. (b) Assuming that these data constitute random samples from four normal populations with the same standard deviation, test at the 0.01 level of significance whether the differences among the four sample means can be attributed to chance.
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(a) Calculate n . s for these data, the
(b) Assuming that these data constitute random samples from four normal populations with the same standard deviation, test at
the 0.01 level of significance whether the differences among the four sample means can be attributed to chance.
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- List the sample space of each experiment. Picking a one-digit numberWhat is meant by the sample space of an experiment?A machine is considered to be unsatisfactory if it produces more than8% defectives. It issuspected that the machine is unsatisfactory. A random sample of 120 items produced bythe machine contains 14 defectives. Does the sample evidence support the claim that themachine is unsatisfactory? Use α = 0.01.
- 6.44 An entomologist is investigating which of two fumigants, F1 or F2, is more effective incontrollingparasities in tobacco plants. To compare the fumigants, nine fields of differingsoil characteristics, drainage, and amount of wind shield were planted with tobacco. Eachfield was then divided into two plots of equal area. Fumigant F1 was randomly assigned toone plot in each field and F2 to the other plot. Fifty plants were randomly selected from eachfield, 25 from each plot, and the numbers of parasites were counted. The data are in the followingtable.Field 1 2 3 4 5 6 7 8 9Fumigant F1 77 40 11 31 28 50 53 26 33Fumigant F2 76 38 10 29 27 48 51 24 32a. What are the populations of interest?b. Do the data provide sufficient evidence to indicate a difference in the meanlevels of parasitesfor the two fumigants? Use a 5 .10. Report the p-value for theexperimental data.c. Estimate the size of the difference in the mean numbers of parasites between thetwo fumigants using a 90% confidence…Suppose that Rob is a quality control specialist at a toothpaste factory. Part of his job is to verify that the filling machines are dispensing the proper amount of toothpaste into each tube. It is his first day working on a new machine that fills travel size toothpaste tubes. The machine is calibrated with an average fill rate of 0.75 ounces of toothpaste per tube. Rob randomly samples 16 of the 1000 travel size tubes of toothpaste that the machine produces that day. The weight, in ounces, of Rob's sample data is presented in the stem-and-leaf plot below. The stems are tenths of an ounce and the leaves are hundredths of an ounce. 5 9 6 6 7 7 8 3 4 8 5 2 3 5 6 8 0 0 0 2 6 6 6 Rob does not know the population standard deviation, so he decides to perform a one-sample t-test to determine if the machine is filling the tubes with the proper amount of toothpaste. Rob knows from past experience that the amount of toothpaste dispensed by similar machines follows a normal distribution very…A researcher used one-factor ANOVA for independent samples to examine the effectiveness of four workout videos. Students who enrolled to the study were divided into four groups with n = 21 participants in each group. Each group exercised to a different workout video and afterwards, all participants completed a survey evaluating the effectiveness of their workout. The partial results of the ANOVA conducted on the collected data are shown in the summary table below: Source SS df MS F Between Treatments 36 ____ ____ F = 4.00 Within Treatments ____ ____ Total ____ A. Fill in all the missing values in the table.…
- 2. Ten spacing treatment were compared in four randomized blocks of ten plots each. The ten spacing were all possible combinations of pairs of inter seedlings distances and the general purpose of the experiment was to investigate both of the effect of changing density seedlings and the effect of spatial arrangement. The plot size is approximately 0.1 hectare. The yield for the plantation (m³ per plot) is recorded in the table below. Block1 Block2 Block3 Block4 Spacing 3.0 x 3.0m 5.95 5.30 6.50 6.35 3.0 x 2.4m 7.10 6.45 6.60 5.75 3.0 x 2.0m 7.00 6.50 6.35 8.90 3.0 x 1.5m 8.10 5.50 6.60 7.50 2.4 x 2.4m 8.85 7.65 7.00 7.90 2.4 x 2.0m 7.65 6.90 8.25 8.30 2.4 x 1.5m 7.80 6.75 8.20 7.25 2.0 x 2.0m 8.05 6.65 8.10 8.05 2.0 x 1.5m 9.30 8.75 8.75 8.00 1.5 x 1.5m 9.35 8.10 7.60 7.75 Perform a complete analysis of variance at 5% level of significance. Discuss your resultThe following tables presents the results of a single factor ANOVA comparing 5 treatment means with n= 10 in each condition. Complete the missing values in the table Source SS df Ms F between treatment 15 Within treatment Total 190Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 30 employees were randomly selected and randomly assigned to the three proposed methods in such a way that each method was used by 10 workers. The number of units assembled correctly was recorded, and the analysis of variance procedure was applied tothe resulting data set. The following results were obtained: SST = 10,800; SSTR = 4560.a. Set up the ANOVA table for this problem.b. Use α = .05 to test for any significant difference in the means for the three assembly methods.
- A sample of 15 maple trees in Vermont were treated with one of three amounts of fertilizer, Low (group 1), Medium (group 2) and High (group 3). The volume in sap (measured in mL) produced by each tree was recorded, and a Single-Factor ANOVA test was performed, which ended up rejecting . The Summary table and the ANOVA table produced by Excel are given below: SUMMARY Groups Count Sum Average Variance Low 5 398.1 79.62 27.572 Medium 5 477.2 95.44 3.703 High 5 445.1 89.02 11.357 ANOVA Source of Variation SS df MS F Between Groups 633.0813333 2 316.5406667 22.27486395 Within Groups 170.528 12 14.21066667 Total 803.6093333 14 If you follow up the ANOVA test with a FORMAL Fisher's LSD Pairwise Comparison (PWC) test on , then use the information provided in the Excel-generated output to calculate the value of the Test Statistic (TS) that you would use to perform this PWC test. Round off your final answer to the…Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 30 employees were randomly selected and randomly assigned to the three proposed methods in such a way that each method was used by10 workers. The number of units assembled correctly was recorded, and the analysis of variance procedure was applied to the resulting data set. The following results were obtained: ; . SST:10,700 SSTR:4500 a. Set up the ANOVA table for this problem (to 2 decimals, if necessary). Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value (to 4 decimals) Treatments…