Questions: 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. 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 μ1 be the mean number of partners for the highest growth region and μ2 be the mean number of partners for the second highest growth region. Determine the hypotheses Choose the correct answer below. A. H0: μ1 ≥ μ2 B. H0: μ1 ≤ μ2 H1: μ1<μ2 H1: μ1>μ2 C. H0: μ1=μ2 D. H0: μ1 ≠ μ2 H1: μ1 ≠ μ2 H1: μ1=μ2

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. 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 μ1 be the mean number of partners for the highest growth region and μ2 be the mean number of partners for the second highest growth region. Determine the hypotheses Choose the correct answer below. A. H0: μ1 ≥ μ2 B. H0: μ1 ≤ μ2 H1: μ1<μ2 H1: μ1>μ2 C. H0: μ1=μ2 D. H0: μ1 ≠ μ2 H1: μ1 ≠ μ2 H1: μ1=μ2
Transcript 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. 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 $\mu_{1}$ be the mean number of partners for the highest growth region and $\mu_{2}$ be the mean number of partners for the second highest growth region. Determine the hypotheses Choose the correct answer below. A. $H_{0} \mu_{1} \geq \mu_{2}$ B. $H_{0} \mu_{1} \leq \mu_{2}$ $H_{1}, \mu_{1}<\mu_{2}$ $H_{1} \cdot \mu_{1}>\mu_{2}$ C. $\mathrm{H}_{0} \mu_{1}=\mu_{2}$ D. $\mathrm{H}_{0} \mu_{1} \neq \mu_{2}$ $H_{1} \mu_{1} \neq \mu_{2}$ $H_{1} \mu_{1}=\mu_{2}$
failed

Solution

failed
failed

Solution Steps

Step 1: Hypotheses

We are testing the following hypotheses:

  • Null Hypothesis: \( H_0: \mu_1 = \mu_2 \) (There is no difference in the mean number of partners between the two regions)
  • Alternative Hypothesis: \( H_1: \mu_1 \neq \mu_2 \) (There is a difference in the mean number of partners between the two regions)
Step 2: Calculate Standard Error

The standard error (SE) is calculated as follows: \[ SE = \sqrt{s_p^2 \left(\frac{1}{n_1} + \frac{1}{n_2}\right)} = 0.4552 \]

Step 3: Calculate Test Statistic

The test statistic \( t \) is computed using the formula: \[ t = \frac{\bar{x}_1 - \bar{x}_2}{SE} = 1.4278 \]

Step 4: Degrees of Freedom

The degrees of freedom \( df \) for the test is given by: \[ df = n_1 + n_2 - 2 = 20 + 20 - 2 = 38 \]

Step 5: Calculate P-value

The P-value is calculated as: \[ P = 2(1 - T(|t|)) = 2(1 - T(1.4278)) = 0.1615 \]

Step 6: Critical Value

The critical value for a two-tailed test at the \( \alpha = 0.05 \) significance level with \( df = 38 \) is: \[ \text{Critical Value} = 2.0244 \]

Step 7: Conclusion

Since the P-value \( 0.1615 \) is greater than the significance level \( \alpha = 0.05 \), we fail to reject the null hypothesis. Therefore, there is no evidence of a difference in the mean number of partners between the two regions.

Final Answer

\(\boxed{\text{Fail to reject } H_0: \text{ There is no evidence of a difference in the mean number of partners between the two regions.}}\)

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
A group of adult males has foot lengths with a mean of 26.69 cm and a standard deviation of 1.16 cm. Use the range rule of thumb for identifying significant values to identify the limits separating values that are significantly low or significantly high. Is the adult male foot length of 23.9 cm significantly low or significantly high? Explain. Significantly low values are cm or lower. (Type an integer or a decimal. Do not round.) Significantly high values are cm or higher. (Type an integer or a decimal. Do not round.) Select the correct choice below and fill in the answer box(es) to complete your choice. A. The adult male foot length of 23.9 cm is significantly high because it is greater than cm. (Type an integer or a decimal. Do not round.) B. The adult male foot length of 23.9 cm is not significant because it is between cm and cm. (Type integers or decimals. Do not round.) C. The adult male foot length of 23.9 cm is significantly low because it is less than cm. (Type an integer or a decimal. Do not round.)
failedAnswered
According to Mill, the ultimate end of utilitarianism is an existence as free of pain as possible and as rich as possible in a. enjoyments. b. social achievement. c. lower pleasures. d. spiritual attainment.
failedAnswered
Can I still get the 3.3L V6 engine on XLT?
failedAnswered
Kevin sold 189 more than twice as much merchandise as Robyn. If Kevin sold at least 45,105, how much did Robyn sell? Write an inequality to represent the facts and solve. Write an inequality to represent the facts. (Type an inequality using x as the variable. Do not simplify. Do not include the symbol in your answer.) Determine how much Robyn sold. (Type an inequality using x as the variable. Simplify your answer. Do not include the symbol in your answer.)
failedAnswered
Graph this line using the slope and y-intercept: y=8x-4