Questions: Math 10 Chapter 7.1 Online Assignment Question 1 We will solve the following problem in steps. "A study is being done by a Company to determine whether the work experience of workers at Branch A is different from the work experience of workers at Branch B. A study of 34 workers at Branch A was conducted and the average years of work experience was 6.5 years. A study of 30 workers at Branch B was conducted and the average years of work experience was 5.5 years. Assume the population standard deviation at Branch A is known to be 1.5 years and the population standard deviation at Branch B is known to be 1.3 years. At α=0.10, can you conclude there is a significance difference in the work experience at the branches?" Let μ1 represent the population work experience of the workers at Branch A. Let μ2 represent the population work experience of the workers at Branch B. What is the null hypothesis? H0: μ1 = μ2 What is the alternative hypothesis? H1: μ1 ≠ μ2 Which test value should you compute? z = (X̄1 - X̄2 - (μ1 - μ2)) / sqrt((σ1^2 / n1) + (σ2^2 / n2))

Math 10 Chapter 7.1 Online Assignment Question 1 We will solve the following problem in steps. "A study is being done by a Company to determine whether the work experience of workers at Branch A is different from the work experience of workers at Branch B. A study of 34 workers at Branch A was conducted and the average years of work experience was 6.5 years. A study of 30 workers at Branch B was conducted and the average years of work experience was 5.5 years. Assume the population standard deviation at Branch A is known to be 1.5 years and the population standard deviation at Branch B is known to be 1.3 years. At α=0.10, can you conclude there is a significance difference in the work experience at the branches?" Let μ1 represent the population work experience of the workers at Branch A. Let μ2 represent the population work experience of the workers at Branch B. What is the null hypothesis? H0: μ1 = μ2 What is the alternative hypothesis? H1: μ1 ≠ μ2 Which test value should you compute? z = (X̄1 - X̄2 - (μ1 - μ2)) / sqrt((σ1^2 / n1) + (σ2^2 / n2))
Transcript text: Math 10 Chapter 7.1 Online Assignment Question 1 We will solve the following problem in steps. "A study is being done by a Company to determine whether the work experience of workers at Branch A is different from the work experience of workers at Branch B. A study of 34 workers at Branch A was conducted and the average years of work experience was 6.5 years. A study of 30 workers at Branch B was conducted and the average years of work experience was 5.5 years. Assume the population standard deviation at Branch A is known to be 1.5 years and the population standard deviation at Branch B is known to be 1.3 years. At $\alpha=0.10$, can you conclude there is a significance difference in the work experience at the branches?" Let $\mu_{1}$ represent the population work experience of the workers at Branch A. Let $\mu_{2}$ represent the population work experience of the workers at Branch B. What is the null hypothesis? \[ H_{0}: \mu_{1} = \mu_{2} \] What is the alternative hypothesis? \[ H_{1}: \mu_{1} \neq \mu_{2} \] Which test value should you compute? $z=\frac{\overline{X_{1}}-\overline{X_{2}}-\left(\mu_{1}-\mu_{2}\right)}{\sqrt{\frac{\sigma_{1}^{2}}{n_{1}}+\frac{\sigma_{2}^{2}}{n_{2}}}}$
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Solution

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Solution Steps

Step 1: Calculate the Standard Error

To determine the standard error \( SE \) of the difference between the two sample means, we use the formula:

\[ SE = \sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}} \]

Substituting the known values:

\[ SE = \sqrt{\frac{1.5^2}{34} + \frac{1.3^2}{30}} = \sqrt{\frac{2.25}{34} + \frac{1.69}{30}} \approx 0.35 \]

Step 2: Calculate the Test Statistic

Next, we calculate the Z-test statistic \( z \) using the formula:

\[ z = \frac{\bar{x}_1 - \bar{x}_2}{SE} \]

Substituting the sample means and the standard error:

\[ z = \frac{6.5 - 5.5}{0.35} \approx 2.857 \]

Step 3: Calculate the P-value

To find the P-value, we use the formula for a two-tailed test:

\[ P = 2 \times (1 - Z(|z|)) \]

Using the calculated \( z \):

\[ P \approx 2 \times (1 - Z(2.857)) \approx 0.0043 \]

Step 4: Conclusion

We compare the P-value with the significance level \( \alpha = 0.10 \):

Since \( P \approx 0.0043 < 0.10 \), we reject the null hypothesis \( H_0: \mu_1 = \mu_2 \).

Final Answer

There is sufficient evidence to conclude that there is a significant difference in the work experience at the branches.

\(\boxed{P \approx 0.0043}\)

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