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Suppose that the proportion of investors who are risk-averse (that is, try to avoid risk in their investment decisions) is though to be at least 0.6. A financial advisor believes that the proportion is actually less than 0.6. A survey of 32 investors found that 20 of them were risk-averse. Formulate a one-sample hypothesis test for a proportion to test this belief. Determine the null hypothesis, H,, and the alternative hypothesis, H,. Ho H,: (Type integers or decimals. Do not round.) Compute the test statistic. (Round to two decimal places as needed.) Find the p-value for the test. (Round to three decimal places as needed.) State the conclusion at the 0.05 level of significance. The p-value is the chosen value of a, so V the null hypothesis. There is V evidence to conclude that the proportion of investors who are risk-averse is not at least 0.6.

Suppose that the proportion of investors who are risk-averse (that is, try to avoid risk in their investment decisions) is though to be at least 0.6. A financial advisor believes that the proportion is actually less than 0.6. A survey of 32 investors found that 20 of them were risk-averse. Formulate a one-sample hypothesis test for a proportion to test this belief. Determine the null hypothesis, H,, and the alternative hypothesis, H,. Ho H,: (Type integers or decimals. Do not round.) Compute the test statistic. (Round to two decimal places as needed.) Find the p-value for the test. (Round to three decimal places as needed.) State the conclusion at the 0.05 level of significance. The p-value is the chosen value of a, so V the null hypothesis. There is V evidence to conclude that the proportion of investors who are risk-averse is not at least 0.6.

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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The image presents a problem related to hypothesis testing in statistics, specifically for proportions. Here’s a detailed explanation suited for an educational website: --- **Problem Context:** Suppose that the proportion of investors who are risk-averse (that is, they try to avoid risk in their investment decisions) is thought to be at least 0.6. A financial advisor believes that the actual proportion is less than 0.6. A survey of 32 investors found that 20 of them were risk-averse. The task is to formulate a one-sample hypothesis test for a proportion to test this belief. --- **Steps for Hypothesis Testing:** 1. **Determine the Null Hypothesis (H₀) and the Alternative Hypothesis (H₁):** - **H₀:** The null hypothesis is that the proportion of risk-averse investors is equal to 0.6. - **H₁:** The alternative hypothesis is that the proportion of risk-averse investors is less than 0.6. 2. **Compute the Test Statistic:** - The test statistic should be calculated by comparing the observed sample proportion with the hypothesized population proportion under the null hypothesis. This would be rounded to two decimal places. 3. **Find the p-value for the test:** - The p-value is the probability that the observed data would occur if the null hypothesis were true. It should be rounded to three decimal places. 4. **State the Conclusion at the 0.05 Level of Significance:** - The conclusion depends on whether the p-value is less than or equal to the chosen significance level (α = 0.05). - If the p-value is less than or equal to 0.05, there is sufficient evidence to reject the null hypothesis, suggesting that the proportion of risk-averse investors is indeed less than 0.6. - If the p-value is greater than 0.05, there is insufficient evidence to reject the null hypothesis. --- This problem allows students to apply concepts of hypothesis testing, specifically regarding proportions, and stresses the importance of understanding statistical significance to interpret results properly.
Transcribed Image Text:The image presents a problem related to hypothesis testing in statistics, specifically for proportions. Here’s a detailed explanation suited for an educational website: --- **Problem Context:** Suppose that the proportion of investors who are risk-averse (that is, they try to avoid risk in their investment decisions) is thought to be at least 0.6. A financial advisor believes that the actual proportion is less than 0.6. A survey of 32 investors found that 20 of them were risk-averse. The task is to formulate a one-sample hypothesis test for a proportion to test this belief. --- **Steps for Hypothesis Testing:** 1. **Determine the Null Hypothesis (H₀) and the Alternative Hypothesis (H₁):** - **H₀:** The null hypothesis is that the proportion of risk-averse investors is equal to 0.6. - **H₁:** The alternative hypothesis is that the proportion of risk-averse investors is less than 0.6. 2. **Compute the Test Statistic:** - The test statistic should be calculated by comparing the observed sample proportion with the hypothesized population proportion under the null hypothesis. This would be rounded to two decimal places. 3. **Find the p-value for the test:** - The p-value is the probability that the observed data would occur if the null hypothesis were true. It should be rounded to three decimal places. 4. **State the Conclusion at the 0.05 Level of Significance:** - The conclusion depends on whether the p-value is less than or equal to the chosen significance level (α = 0.05). - If the p-value is less than or equal to 0.05, there is sufficient evidence to reject the null hypothesis, suggesting that the proportion of risk-averse investors is indeed less than 0.6. - If the p-value is greater than 0.05, there is insufficient evidence to reject the null hypothesis. --- This problem allows students to apply concepts of hypothesis testing, specifically regarding proportions, and stresses the importance of understanding statistical significance to interpret results properly.
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