You may need to use the appropriate technology to answer this question. Periodically, customers of a financial services company are asked to evaluate the company's financial consultants and services. Higher ratings on the client satisfaction survey indicate better service, with 7 the maximum service rating. Independent samples of service ratings for two financial consultants are summarized here. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. Use a- 0.05 and test to see whether the consultant with more experience has the higher population mean service rating. ConsultantA Consultant B n- 16 n2- 10 x - 6.83 x2 - 6.28 $- 0.68 52- 0.75 (a) State the null and alternative hypotheses. O Ho: H1 - H2 * 0 O Hoi H, - H2>o O Mo: H-Hzso O Ho: H- H2-0 O Mo: H - H2so (b) Compute the value of the test statistic. (Round your answer to three decimal places.) (c) What is the p-value? (Round your answer to four decimal places.) nuvalue

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**Evaluating Financial Consultant Experience on Service Ratings**

Periodically, customers of a financial services company are asked to evaluate the company's financial consultants and services. Higher ratings on the client satisfaction survey indicate better service, with 7 as the maximum service rating. Independent samples of service ratings for two financial consultants are summarized below. Consultant A has 10 years of experience, whereas Consultant B has 1 year of experience. Use a significance level of α = 0.05 to test whether the consultant with more experience has the higher population mean service rating.

**Summary Table:**

|                 | Consultant A | Consultant B |
|-----------------|--------------|--------------|
| Sample size     | \(n_1 = 16\) | \(n_2 = 10\) |
| Mean rating     | \(\bar{x}_1 = 6.83\) | \(\bar{x}_2 = 6.28\) |
| Standard deviation | \(s_1 = 0.68\) | \(s_2 = 0.75\) |

**Tasks:**

(a) **State the Null and Alternative Hypotheses:**

- \(\text{H}_0: \mu_1 - \mu_2 = 0\)
- \(\text{H}_a: \mu_1 - \mu_2 > 0\)

(b) **Compute the Value of the Test Statistic:**

- Calculate and round your answer to three decimal places.

(c) **Calculate the p-value:**

- Round your answer to four decimal places.

These analytical steps will help determine if the difference in years of experience significantly affects the service ratings of the consultants.
Transcribed Image Text:**Evaluating Financial Consultant Experience on Service Ratings** Periodically, customers of a financial services company are asked to evaluate the company's financial consultants and services. Higher ratings on the client satisfaction survey indicate better service, with 7 as the maximum service rating. Independent samples of service ratings for two financial consultants are summarized below. Consultant A has 10 years of experience, whereas Consultant B has 1 year of experience. Use a significance level of α = 0.05 to test whether the consultant with more experience has the higher population mean service rating. **Summary Table:** | | Consultant A | Consultant B | |-----------------|--------------|--------------| | Sample size | \(n_1 = 16\) | \(n_2 = 10\) | | Mean rating | \(\bar{x}_1 = 6.83\) | \(\bar{x}_2 = 6.28\) | | Standard deviation | \(s_1 = 0.68\) | \(s_2 = 0.75\) | **Tasks:** (a) **State the Null and Alternative Hypotheses:** - \(\text{H}_0: \mu_1 - \mu_2 = 0\) - \(\text{H}_a: \mu_1 - \mu_2 > 0\) (b) **Compute the Value of the Test Statistic:** - Calculate and round your answer to three decimal places. (c) **Calculate the p-value:** - Round your answer to four decimal places. These analytical steps will help determine if the difference in years of experience significantly affects the service ratings of the consultants.
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