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Question 1 Exercise 12-2 Consider a multinomial experiment with n = 340 and k = 3. The null hypothesis is H0: p1 = 0.60, p2 = 0.25, and p3 = 0.15. The observed frequencies resulting from the experiment are: Category 1 2 3 Frequency 230 80 30 ________________________________________ (Use Table 3) a. Choose the appropriate alternative hypothesis. All population proportions differ from their hypothesized values. At least one of the population proportions differs from its hypothesized value. b-1. Calculate the value of the test statistic.(Round intermediate calculations to 4 decimal places and your final answer to 2 decimal places.) Test statistic b-2. Approximate the p-value. 0.025 < p-value < 0.050 p-value < 0.005 0.005 < p-value < 0.010 0.010 < p-value < 0.025 0.050 < p-value < 0.100 c. At the 1% significance level, what is the conclusion to the hypothesis test? Do not reject H0 since the p-value is more than α. Reject H0 since the p-value is less than α. Reject H0 since the p-value is more than α. Do not reject H0 since the p-value is less than α. Question 3 Exercise 13-1 A random sample of five observations from three treatments produced the following data: Use Table 4. Treatments A B C 22 24 26 30 30 23 29 16 18 21 20 22 26 25 16 = 25.6 = 23.0 = 21.0 sA2 = 16.3 sB2 = 28.0 sC2 = 16.0 ________________________________________ a. Calculate the grand mean. (Round your answer to 2 decimal places.) Grand mean b. Calculate SSTR and MSTR. (Round intermediate values to 4 decimal places and final answers to 2 decimal places.) SSTR MSTR ________________________________________ c. Calculate SSE and MSE. (Round intermediate values to 4 decimal places and final answers to 2 decimal places.) SSE MSE ________________________________________ d. Specify the competing hypotheses in order to determine whether some differences exist between the population means. H0: μA ≤ μB ≤ μC; HA: Not all population means are equal. H0: μA ≥ μB ≥ μC; HA: Not all population means are equal. H0: μA = μB = μC; HA: Not all population means are equal. e. Calculate the value of the F(df1,df2) test statistic. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Test statistic f. Using the critical value approach at the 1% significance level, what is the conclusion to the test? Reject H0 since the value of the test statistic exceeds 6.93. Reject H0 since the value of the test statistic exceeds 5.52. Do not reject H0 since the value of the test statistic does not exceed 5.52. Do not reject H0 since the value of the test statistic does not exceed 6.93. Question 5 Exercise 12-17 The following sample data reflect shipments received by a large firm from three different vendors. Use Table 3. Vendor Defective Acceptable 1 16 132 2 14 78 3 25 233 ________________________________________ a. Choose the competing hypotheses to determine whether quality is associated with the source of the shipments. H0: Quality and source of shipment (vendor) are dependent.; HA: Quality and source of shipment (vendor) are independent. H0: Quality and source of shipment (vendor) are independent.; HA: Quality and source of shipment (vendor) are dependent. b-1. Calculate the value of the test statistic.(Round intermediate calculations to 4 decimal places and your final answer to 2 decimal places.) χ2df b-2. Specify the decision rule at a 5% significance level. (Round your answer to 3 decimal places.) Reject H0 if χ2df > b-3. What is your conclusion? Reject H0; quality and source of shipment are dependent Do not reject H0; quality and source of shipment are dependent Reject H0; quality and source of shipment are not dependent Do not reject H0; quality and source of shipment are not dependent c. Should the firm be concerned about the source of the shipments? Yes No Question 7 Exercise 12-21 Consider the following sample data with mean and standard deviation of 17.5 and 7.4, respectively. UseTable 3. Class Frequency Less than 10 29 10 up to 20 95 20 up to 30 60 30 or more 17 n = 201 ________________________________________ a. Using the goodness-of-fit test for normality, specify the competing hypotheses in order to determine whether or not the data are normally distributed. H0: The data are normally distributed with a mean of 17.5 and a standard deviation of 7.4.; HA: The data are not normally distributed with a mean of 17.5 and a standard deviation of 7.4. H0: The data are not normally distributed with a mean of 17.5 and a standard deviation of 7.4.; HA: The data are normally distributed with a mean of 17.5 and a standard deviation of 7.4. b. Calculate the value of the test statistic. (Round the z value to 2 decimal places, all other intermediate values to 4 decimal places, and final answer to 2 decimal places.) χ2df c. At the 5.0% significance level, what is the decision rule? (Round your answer to 3 decimal places.) Reject H0 if χ2df > d. What is the conclusion? Do not reject H0; the data are normally distributed Reject H0; the data are normally distributed Do not reject H0; the data are not normally distributed Reject H0; the data are not normally distributed Exercise 12-11 Suppose you are conducting a test of independence. Specify the critical value under the following scenarios (Use Table 3): a. rows = 5, columns = 2, and α = 0.01. (Round your answer to 3 decimal places.) Critical value b. rows = 2, columns = 2, and α = 0.01. (Round your answer to 3 decimal places.) Critical value Question 9 Exercise 12-1 Consider a multinomial experiment with n = 276 and k = 4. The null hypothesis to be tested is H0: p1 = p2= p3 = p4 = 0.25. The observed frequencies resulting from the experiment are (Use Table 3): Category 1 2 3 4 Frequency 76 46 78 76 ________________________________________ a. Choose the appropriate alternative hypothesis. Not all population proportions are equal to 0.25. All population proportions differ from 0.25. b. Calculate the value of the test statistic.(Round intermediate calculations to 4 decimal places and your final answer to 2 decimal places.) χ2df c. Calculate the critical value at a 5% significance level. (Round your answer to 3 decimal places.) χ2α,df d. What is the conclusion to the hypothesis test? Reject H0 since the value of the test statistic does not exceed the critical value Do not reject H0 since the value of the test statistic does not exceed the critical value Reject H0 since the value of the test statistic exceeds the critical value Do not reject H0 since the value of the test statistic exceeds the critical value Exercise 13-35 The effects of detergent brand name (factor A) and the temperature of the water (factor B) on the brightness of washed fabrics are being studied. Four brand names and two temperature levels are used, and six replicates for each combination are examined. The following ANOVA table is produced. ANOVA Source of Variation SS df MS F p-value F crit Sample 87 1 87.00 85.80 1.68E-11 4.085 Columns 134.44 3 44.81 44.19 9.08E-13 2.839 Interaction 7.62 3 2.54 2.50 .0728 2.839 Within 40.56 40 1.01 ________________________________________ ________________________________________ Total 269.62 47 ________________________________________________________________________________ ________________________________________________________________________________ ________________________________________ a. Can you conclude that there is interaction between detergent brand name and the temperature of the water at the 5% significance level? No Yes b-1. Are you able to conduct tests based on the main effects? Yes No b-2. If yes, conduct these tests at the 5% significance level. (You may select more than one answer. Single click the box with the question mark to produce a check mark for a correct answer and double click the box with the question mark to empty the box for a wrong answer.) Differences exist in the average brightness of fabrics depending on the temperature of the water. Differences do not exist in the average brightness of fabrics depending on the detergent brand name. Differences exist in the average brightness of fabrics depending on the detergent brand name. Differences do not exist in the average brightness of fabrics depending on the temperature of the water.

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Answer 1:

a. Part b, at least one of the proportions differs

b. 1. The test statistic is found as:
Total frequency = 340
P1=0.60, p2= 0.25, p3 = 0.15
Expected frequency, for category 1 = 0.60 *340 = 204, fr category 2 = 0.25 * 340 = 85 and for category 3 = 340 – 204 – 85 = 51.
Actual frequency = 230, 80, 30.
Test statistic = (204 – 230)2/204 + (85 – 80)2/85 + (51 – 30)2/51 = 12.25
2. (b) p < 0.005...
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