Inference about parameters for two population variances of/02 (CH7) 1. (5 points) A formal comparison between a new microbial method for the detection of E. coli, the Petrifilm HEC test, and an elaborate laboratory-based procedure, hydrophobic grid membrane filtration (HGMF), will now be described. However, it was necessary to compare the performance of the HEC test to that of the HGMF procedure in order to determine if the HEC test might be a viable method for detecting E. coli Table. E. coli readings (Log10CFU/ml) from HGMF and HEC. Because the objective of the study was to evaluate the HEC procedure for its performance in detecting E. coli, it is necessary to evaluate its repeatability and its agreement with an accepted method for E. coli-namely, the HGMF procedure. Thus, we need to compare both the level and the variability in the two methods for determining E. coli concentrations. That is, we will need to test hypotheses about both the means and the standard deviations of HEC and HGMF E. coli concentrations. We had 24 independent observations from the HEC and HGMF procedures on pure cultures of E. coli having a specified Sample HGMF HEC Sample HGMF HEC 6.65 6.67 13 6.94 711 6.62 6.75 WINE 14 703 714 6.68 6.83 15 705 714 6.71 6.87 16 7,06 7.23 6.77 6.95 17 707 725 6.79 6.98 18 209 7.28 6.79 703 19 211 7.34 6.81 705 20 712 7.37 6.89 708 21 7.16 739 10 6.90 709 22 728 7.45 11 6.92 7.09 23 729 7.58 12 6.93 711 24 730 7.54 Table of HEC and HGMF summary statistics Sample Standard Procedure Size Mean Deviation HEC 24 7.1383 2358 HGMF 24 6.9567 2029 Analyzing the Data and Interpreting the analyses using the point estimationa. (1 point) Set up Research hypothesis, Null hypothesis The research hypothesis is that the mean plant density for the control plots exceeds that for the oil-spill plots. b. (1 point) Choose the right Test statistics, TS, calculate the test statistics c. (1 point) Find the critical value of the test statistics and draw conclusion d. (1 point) Check assumptions and draw conclusions. Please comment on the normality condition using the provided Normal probability plots and boxplots for HEC and HGMF. 99 70 60 - 6 700 Percent 50 - 40- 30- 20 - 10 HGMF HEC 65 6.6 67 63 69 70 7.1 72 7.3 T.A () E call concentration with HOME 70- 60- Percent 50- 30 - 20 - 6 50 6.75 7,00 7.35 7.50 7.75 (bi E. call concentration with HEC Figs. Normal probability plots and boxplots for HGMF and HEC e. (1 point) Construct a 95% confidence interval for & and comment on these values relating to the test decision1. (5 points + Extra 1 point) An experimenter is interested in the effect of music on memory for words. The data are shown in the below table. There are fifteen observations. Each score represents the number of words recalled. Please analyze the data using the appropriate statistical test and determine whether there is a difference in means of the number of words recalled in the country, classical, and blues music. Given the significance level, a = 0.05. Country Classical Blues 3 5 9 2 3 5 2 2 7 2 4 ANOVA Source of Variation SS MS F P-value F crit Between Groups 89.2 ? 0 Within Groups 16.8 12 Total 106 14 a. (1 point) Summarizing the Data: Descriptive Statistics for data. b. (1 point) Please use excel add-in tool "Data Anlysis-Avova: Single" to construct the ANOVA table According to the AVOVA Table. Please fill in the Mean squares between groups and within groups in the ANOVA table. (Hint: MSB SSB/dj(wem, MSW-SSW/ djwithin) c. (1 point) State the Null Ho, & Alternative Hypotheses Hi d. (1 point) Set the significance level a, dfl, df2, and determine Farit (Hint: Please use o, dfl and df2 to find Feri using the provided F table) e. (1 point) Select the appropriate statistics from the following test, z, t, F, and compute it. Please write down the calculation steps. f. (Extral point) Why do we use ANOVA rather than multiple t-tests to test the equality of more than three population means