BNAD277 Chapter 12 Notes
BNAD277 Chapter 12 Notes BNAD277
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This 5 page Class Notes was uploaded by Kristin Koelewyn on Saturday March 19, 2016. The Class Notes belongs to BNAD277 at University of Arizona taught by Dr. S. Umashankar in Spring 2016. Since its upload, it has received 26 views. For similar materials see Business Statistics in Business at University of Arizona.
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Date Created: 03/19/16
Bnad277: Chapter 12 Notes Tests of Goodness of Fit, Independence, and Multiple Proportions: - In this chapter we introduce three additional hypothesis-testing procedures. 2 - The test statistic and the distribution used are based on the chi-square (c ) distribution. - In all cases, the data are categorical. - Goodness of Fit Test: Multinomial Probability Distribution: o 1. State the null and alternative hypotheses: o 2. Select a random sample and record the observed frequency, f , i for each of the k categories. o 3. Assuming H is t0ue, compute the expected frequency, e , in i each category by multiplying the category probability by the sample size. o 4. Compute the value of the test statistic. o 5. Rejection Rule: o Example: Finger Lakes Homes manufactures four models of prefabricated homes, a two-story colonial, a log cabin, a split-level, and an A-frame. To help in production planning, management would like to determine if previous customer purchases indicate that there is a preference in the style selected. ▯ The number of homes sold of each model for 100 sales over the past two years is shown below. ▯ Hypotheses: 2 ▯ Reject Rule: Reject H i0 p-value </ .05 or x > 7.815 ▯ Conclusion Using the Critical Value Approach: • X = 10 >/ 7.815 • We reject, at the .05 level of significance, the assumption that there is no home-style preference. - Test of Independence: o 1. Set up the null and alternative hypotheses. o 2. Select a random sample and record the observed frequency, f , ij for each cell of the contingency table. o 3. Compute the expected frequency, e , for eijh cell. o 4. Compute the test statistic: o 5. Determine the rejection rule: - Testing the Equality of Population Proportions for Three or More Populations: o Using the notation ▯ p1= population proportion for population 1 ▯ p 2 population proportion for population 2 ▯ and p k population proportion for population k o The hypotheses for the equality of population proportions for k > 3 populations are as follows: o If H c0nnot be rejected, we cannot detect a difference among the k population proportions. o If H c0n be rejected, we can conclude that not all k population proportions are equal. o Further analyses can be done to conclude which population proportions are significantly different from others. ▯ Example: Finger Lakes Homes manufactures three models of prefabricated homes, a two-story colonial, a log cabin, and an A-frame. To help in product-line planning, management would like to compare the customer satisfaction with the three home styles. ▯ p1= proportion likely to repurchase a Colonial for the population of Colonial owners ▯ p2= proportion likely to repurchase a Log Cabin for the population of Log Cabin owners ▯ p3= proportion likely to repurchase an A-Frame for the population of A-Frame owners ▯ Observed Frequencies: ▯ Next, determine the expected frequencies under the assumption H is0correct. ▯ Expected Frequencies: ▯ Next, compute the value of the chi-square test statistic: ▯ Computation of the Chi-Square Test Statistic: 2 ▯ Rejection Rule: Because c = 8.670 is between 9.210 and 7.378, the area in the upper tail of the distribution is between .01 and .025. ▯ The p-value < a. We can reject the null hypothesis. ▯ We have concluded that the population proportions for the three populations of home owners are not equal. ▯ To identify where the differences between population proportions exist, we will rely on a multiple comparisons procedure. - Multiple Comparisons Procedure: o We begin by computing the three sample proportions: o We will use a multiple comparison procedure known as the Marascuillo procedure. o Marascuillo Procedure: We compute the absolute value of the pair wise difference between sample proportions: o For each pair-wise comparison compute a critical value as follows: o Pair-wise Comparison Tests:
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