Transcribed Image Text: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 Ha be the mean number of partners for the second highest growth region. Determine the hypotheses. Choose the correct answer below.
A. Ho: H1 = H2
O B. Ho: H12H2
H1: H1 # H2
H1: H1 <H2
O C. Ho: H1 SH2
H1: 41> H2
O D. Ho: H1 H2
H1: H1 = H2
Determine the test statistic.
tSTAT = - 1.09 (Round to two decimal places as needed.)
Accounting firms data
Determine the critical value(s).
- 2.02, 2.02
Number of partners for 20 firms in the region with the highest
combined growth
(Use a comma to separate answers as needed. Round to two decimal places as needed.)
Choose the correct conclusion below.
73 101 29
29
38
22 34
23 34
12
9 7 9
12
17
25
11
29
15
Number of partners for 20 firms in the region with the second
O A. Reject Ho. There is sufficient evidence that the means differ.
highest combined growth
B. Do not reject Ho. There is sufficient evidence that the means differ.
171
47
35
53
41
10
35
41
32
20
31
18
11 35
35
14
36
27
27
19
O C. Reject Ho. There is insufficient evidence that the means differ.
D. Do not reject Ho. There is insufficient evidence that the means differ.
b. Find the p-value in (a) and interpret its meaning.
Print
Done
p-value =
(Round to three decimal places as needed.)
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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