A recent survey identified the top accounting firms within 10 geographical regions across country X. The top 2 regions reported a combined growth of 19% and 18%. A characteristic description of the accounting firms in these two regions included the number of partners in the firms. Attached below is a sample of the number of partners for 20 firms for each region. Complete (a) through (c) below. E Click the icon to view the accounting firms data. a. At the 0.05 level of significance when pooling the variances, is there evidence of a difference between the two regions' accounting firms with respect to the mean number of partners? Let u, be the mean number of partners for the highest growth region and 42 be the mean number of partners for the second highest growth region. Determine the hypotheses. Choose the correct answer below. A. Ho: H1 =P2 OB. Ho: 12 P2 H: 42 OC. Ho: H1 SP2 H: 1 > H2 OD. Ho: 1 #P2 H: H1 =2 Determine the test statistic. tSTAT = (Round to two decimal places as needed.) Accounting firms data Number of partners for 20 firms in the region with the highest combined growth 73 101 29 29 38 22 34 23 34 12 9 7 9 12 17 25 11 15 29 9 Number of partners for 20 firms in the region with the second highest combined growth 171 47 35 53 41 10 35 41 32 20 31 18 11 35 35 14 36 27 27 19
A recent survey identified the top accounting firms within 10 geographical regions across country X. The top 2 regions reported a combined growth of 19% and 18%. A characteristic description of the accounting firms in these two regions included the number of partners in the firms. Attached below is a sample of the number of partners for 20 firms for each region. Complete (a) through (c) below. E Click the icon to view the accounting firms data. a. At the 0.05 level of significance when pooling the variances, is there evidence of a difference between the two regions' accounting firms with respect to the mean number of partners? Let u, be the mean number of partners for the highest growth region and 42 be the mean number of partners for the second highest growth region. Determine the hypotheses. Choose the correct answer below. A. Ho: H1 =P2 OB. Ho: 12 P2 H: 42 OC. Ho: H1 SP2 H: 1 > H2 OD. Ho: 1 #P2 H: H1 =2 Determine the test statistic. tSTAT = (Round to two decimal places as needed.) Accounting firms data Number of partners for 20 firms in the region with the highest combined growth 73 101 29 29 38 22 34 23 34 12 9 7 9 12 17 25 11 15 29 9 Number of partners for 20 firms in the region with the second highest combined growth 171 47 35 53 41 10 35 41 32 20 31 18 11 35 35 14 36 27 27 19
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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Transcribed Image Text:## Educational Content: Analyzing Accounting Firm Data
**Overview**
A recent survey highlighted the top accounting firms across 10 geographical regions in country X, where the top 2 regions reported combined growth rates of 19% and 18%. The following analysis focuses on the number of partners within these firms. You are presented with data on the number of partners for 20 firms in each region and are asked to perform a statistical analysis.
**Objective**
At a 0.05 level of significance, investigate whether there is a difference in the mean number of partners between the two regions' accounting firms.
**Hypothesis Formulation**
Define:
- \( \mu_1 \): Mean number of partners for the region with the highest growth.
- \( \mu_2 \): Mean number of partners for the second highest growth region.
Choose the correct hypotheses to test:
- Option A:
- \( H_0: \mu_1 = \mu_2 \)
- \( H_1: \mu_1 \neq \mu_2 \)
- Option B:
- \( H_0: \mu_1 \geq \mu_2 \)
- \( H_1: \mu_1 < \mu_2 \)
- Option C:
- \( H_0: \mu_1 \leq \mu_2 \)
- \( H_1: \mu_1 > \mu_2 \)
- Option D:
- \( H_0: \mu_1 \neq \mu_2 \)
- \( H_1: \mu_1 = \mu_2 \)
Selected Hypotheses: Option A
**Data Provided**
- For the region with the highest combined growth:
- Partners per 20 firms: 73, 101, 29, 38, 29, 32, 38, 32, 34, 12, 9, 7, 9, 12, 17, 25, 11, 25, 29, 9
- For the region with the second highest combined growth:
- Partners per 20 firms: 171, 47, 53, 31, 65, 53, 51, 33, 47, 32, 19, 21, 32, 27, 35,
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