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Find the value of the test statistic. (Round your answer to two decimal places.)

Find the value of the test statistic. (Round your answer to two decimal places.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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### Hypothesis Testing on Bullish and Bearish Sentiment A professional association of investors conducts a weekly survey of its members to measure the percentage who are bullish, bearish, and neutral on the stock market for the next six months. The survey results showed 38.1% bullish, 22.8% neutral, and 39.1% bearish. These results are based on a sample of 300 members. #### (a) Bullish Sentiment Hypothesis Test **Problem Statement:** Over the long term, the proportion of bullish members is 0.39. Conduct a hypothesis test at the 5% level of significance to determine if the current sample results show that the bullish sentiment differs from its long-term average of 0.39. What are your findings? **Formulate the Hypotheses:** 1. \(H_0: p = 0.39\) 2. \(H_1: p \ne 0.39\) **Steps to Solve:** 1. **Find the test statistic.** (Round your answer to two decimal places.) 2. **Find the p-value.** (Round your answer to four decimal places.) - p-value = **Conclusion Statements:** - Reject \(H_0\): There is sufficient evidence to conclude that the bullish sentiment differs from its long-term average of 0.39. - Do not reject \(H_0\): There is sufficient evidence to conclude that the bullish sentiment does not differ from its long-term average of 0.39. - Do not reject \(H_0\): There is insufficient evidence to conclude that the bullish sentiment differs from its long-term average of 0.39. - Reject \(H_0\): There is insufficient evidence to conclude that the bullish sentiment differs from its long-term average of 0.39. #### (b) Bearish Sentiment Hypothesis Test **Problem Statement:** Over the long term, the proportion of bearish members is 0.30. Conduct a hypothesis test at the 1% level of significance to determine if the current sample results show that bearish sentiment is above its long-term average of 0.30. What are your findings? **Note: Since the image does not display the completion of parts (a) and (b), the test statistic, p-value, and specific findings are not provided. You would need to calculate the test statistics and p-values using appropriate statistical methods to draw
Transcribed Image Text:### Hypothesis Testing on Bullish and Bearish Sentiment A professional association of investors conducts a weekly survey of its members to measure the percentage who are bullish, bearish, and neutral on the stock market for the next six months. The survey results showed 38.1% bullish, 22.8% neutral, and 39.1% bearish. These results are based on a sample of 300 members. #### (a) Bullish Sentiment Hypothesis Test **Problem Statement:** Over the long term, the proportion of bullish members is 0.39. Conduct a hypothesis test at the 5% level of significance to determine if the current sample results show that the bullish sentiment differs from its long-term average of 0.39. What are your findings? **Formulate the Hypotheses:** 1. \(H_0: p = 0.39\) 2. \(H_1: p \ne 0.39\) **Steps to Solve:** 1. **Find the test statistic.** (Round your answer to two decimal places.) 2. **Find the p-value.** (Round your answer to four decimal places.) - p-value = **Conclusion Statements:** - Reject \(H_0\): There is sufficient evidence to conclude that the bullish sentiment differs from its long-term average of 0.39. - Do not reject \(H_0\): There is sufficient evidence to conclude that the bullish sentiment does not differ from its long-term average of 0.39. - Do not reject \(H_0\): There is insufficient evidence to conclude that the bullish sentiment differs from its long-term average of 0.39. - Reject \(H_0\): There is insufficient evidence to conclude that the bullish sentiment differs from its long-term average of 0.39. #### (b) Bearish Sentiment Hypothesis Test **Problem Statement:** Over the long term, the proportion of bearish members is 0.30. Conduct a hypothesis test at the 1% level of significance to determine if the current sample results show that bearish sentiment is above its long-term average of 0.30. What are your findings? **Note: Since the image does not display the completion of parts (a) and (b), the test statistic, p-value, and specific findings are not provided. You would need to calculate the test statistics and p-values using appropriate statistical methods to draw
### Statistical Hypothesis Testing on Current Bearish Sentiment In this educational segment, we are focusing on statistical hypothesis testing to determine whether the current bearish sentiment is above its long-term average of 0.30. The following steps and conclusions are illustrated to aid in understanding the process. #### Formulating the Hypotheses We start by formulating the null and alternative hypotheses. Here are possible hypotheses for this scenario: 1. \( H_0: p \leq 0.30 \), \( H_a: p > 0.30 \) 2. \( H_0: p > 0.30 \), \( H_a: p \leq 0.30 \) 3. \( H_0: p \geq 0.30 \), \( H_a: p < 0.30 \) 4. \( H_0: p < 0.30 \), \( H_a: p \geq 0.30 \) 5. \( H_0: p = 0.30 \), \( H_a: p \neq 0.30 \) 6. \( H_0: p \neq 0.30 \), \( H_a: p = 0.30 \) The correct formulation for determining whether the current bearish sentiment is significantly above its long-term average of 0.30 is: \[ H_0: p \leq 0.30, \quad H_a: p > 0.30 \] #### Finding the Test Statistic The next step is to find the test statistic. (Students would be shown the process of calculation with examples and formulas here. It is essential to round the answer to two decimal places). #### Finding the p-value After obtaining the test statistic, the p-value can be calculated. (This involves statistical software or p-value tables, and answers are rounded to four decimal places). \[ \text{p-value} = \] #### Drawing Conclusions Based on the computed p-value, we can draw one of the following conclusions: - Do not reject \( H_0 \): There is sufficient evidence to conclude that the bearish sentiment is not above its long-term average of 0.30. - Reject \( H_0 \): There is sufficient evidence to conclude that the bearish sentiment is above its long-term average of 0.30. In conclusion: - Do not reject \( H_0 \): There is insufficient evidence to conclude
Transcribed Image Text:### Statistical Hypothesis Testing on Current Bearish Sentiment In this educational segment, we are focusing on statistical hypothesis testing to determine whether the current bearish sentiment is above its long-term average of 0.30. The following steps and conclusions are illustrated to aid in understanding the process. #### Formulating the Hypotheses We start by formulating the null and alternative hypotheses. Here are possible hypotheses for this scenario: 1. \( H_0: p \leq 0.30 \), \( H_a: p > 0.30 \) 2. \( H_0: p > 0.30 \), \( H_a: p \leq 0.30 \) 3. \( H_0: p \geq 0.30 \), \( H_a: p < 0.30 \) 4. \( H_0: p < 0.30 \), \( H_a: p \geq 0.30 \) 5. \( H_0: p = 0.30 \), \( H_a: p \neq 0.30 \) 6. \( H_0: p \neq 0.30 \), \( H_a: p = 0.30 \) The correct formulation for determining whether the current bearish sentiment is significantly above its long-term average of 0.30 is: \[ H_0: p \leq 0.30, \quad H_a: p > 0.30 \] #### Finding the Test Statistic The next step is to find the test statistic. (Students would be shown the process of calculation with examples and formulas here. It is essential to round the answer to two decimal places). #### Finding the p-value After obtaining the test statistic, the p-value can be calculated. (This involves statistical software or p-value tables, and answers are rounded to four decimal places). \[ \text{p-value} = \] #### Drawing Conclusions Based on the computed p-value, we can draw one of the following conclusions: - Do not reject \( H_0 \): There is sufficient evidence to conclude that the bearish sentiment is not above its long-term average of 0.30. - Reject \( H_0 \): There is sufficient evidence to conclude that the bearish sentiment is above its long-term average of 0.30. In conclusion: - Do not reject \( H_0 \): There is insufficient evidence to conclude
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