A well-known brokerage firm executive claimed that 90% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 300 people, 276 of them said they are confident of meeting their goals. Test the claim that the proportion of people who are confident is larger than 90% at the 0.05 significance level. The pull

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**Hypothesis Testing: Investor Confidence in Meeting Investment Goals**

A well-known brokerage firm executive claimed that 90% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 300 people, 276 of them said they are confident of meeting their goals.

**Objective:** 
Test the claim that the proportion of people who are confident is larger than 90% at the 0.05 significance level.

**Step 1: Formulate Hypotheses**

The null and alternative hypotheses would be:
- \( H_0 : p = 0.9 \) 
- \( H_1 : p > 0.9 \)

**Step 2: Choose the Test Type**

The test is:
- Right-tailed
- Two-tailed
- Left-tailed

**Step 3: Calculate Test Statistic**

The test statistic is: \( \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \) (to 3 decimals)

**Step 4: Determine the P-value**

The p-value is: \( \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \) (to 4 decimals)
  
**Step 5: Make a Decision**

Based on this we:
- Fail to reject the null hypothesis
- Reject the null hypothesis

**Submit your decision.**

*(End of the questionnaire)*
Transcribed Image Text:**Hypothesis Testing: Investor Confidence in Meeting Investment Goals** A well-known brokerage firm executive claimed that 90% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 300 people, 276 of them said they are confident of meeting their goals. **Objective:** Test the claim that the proportion of people who are confident is larger than 90% at the 0.05 significance level. **Step 1: Formulate Hypotheses** The null and alternative hypotheses would be: - \( H_0 : p = 0.9 \) - \( H_1 : p > 0.9 \) **Step 2: Choose the Test Type** The test is: - Right-tailed - Two-tailed - Left-tailed **Step 3: Calculate Test Statistic** The test statistic is: \( \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \) (to 3 decimals) **Step 4: Determine the P-value** The p-value is: \( \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \) (to 4 decimals) **Step 5: Make a Decision** Based on this we: - Fail to reject the null hypothesis - Reject the null hypothesis **Submit your decision.** *(End of the questionnaire)*
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