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Do rats take more time on average than hamsters to travel through a maze? The table below shows the times in seconds that the rats and hamsters took. Rats: 12, 30, 34, 42, 28, 20, 47, 33, 24, 53 Hamsters: 33, 29, 23, 15, 19, 20, 42, 25 Assume that both populations follow a normal distribution. What can be concluded at the a = 0.01 level of significance level of significance?

Do rats take more time on average than hamsters to travel through a maze? The table below shows the times in seconds that the rats and hamsters took. Rats: 12, 30, 34, 42, 28, 20, 47, 33, 24, 53 Hamsters: 33, 29, 23, 15, 19, 20, 42, 25 Assume that both populations follow a normal distribution. What can be concluded at the a = 0.01 level of significance level of significance?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
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### Analyzing Maze Completion Times for Rats and Hamsters **Objective:** To determine if rats take more time on average than hamsters to travel through a maze. **Data Set:** - **Rats' Times (in seconds):** 12, 30, 34, 42, 28, 20, 47, 33, 24, 53 - **Hamsters' Times (in seconds):** 33, 29, 23, 15, 19, 20, 42, 25 Assume both populations follow a normal distribution. Analyze the data using a significance level, \(\alpha = 0.01\). **Steps for Analysis:** 1. **Select the Test** Choose the appropriate statistical test to compare the means of two independent samples. 2. **Formulate Hypotheses:** - **Null Hypothesis (\(H_0\)):** No difference in the mean times between rats and hamsters. - **Alternative Hypothesis (\(H_1\)):** Rats take more time on average than hamsters. 3. **Calculate the Test Statistic (\(t\)):** Compute the test statistic with precision up to three decimal places. 4. **Determine the P-value** Calculate the p-value, providing the result up to four decimal places. 5. **Compare P-value to \(\alpha\):** - Determine whether the p-value is less than or equal to \(\alpha\). 6. **Draw Conclusions:** - If the test results are statistically significant (\(p \leq \alpha\)), conclude there is sufficient evidence that rats take more time. - If not, conclude there is insufficient evidence. **Final Conclusion Options:** - The results indicate a significant difference at \(\alpha = 0.01\), allowing us to infer that rats take more time than hamsters. - The results are statistically insignificant, providing evidence that the times are equal. - The results are insignificant, indicating insufficient evidence for a difference in time. Complete the calculations and select the correct options based on your analysis results.
Transcribed Image Text:### Analyzing Maze Completion Times for Rats and Hamsters **Objective:** To determine if rats take more time on average than hamsters to travel through a maze. **Data Set:** - **Rats' Times (in seconds):** 12, 30, 34, 42, 28, 20, 47, 33, 24, 53 - **Hamsters' Times (in seconds):** 33, 29, 23, 15, 19, 20, 42, 25 Assume both populations follow a normal distribution. Analyze the data using a significance level, \(\alpha = 0.01\). **Steps for Analysis:** 1. **Select the Test** Choose the appropriate statistical test to compare the means of two independent samples. 2. **Formulate Hypotheses:** - **Null Hypothesis (\(H_0\)):** No difference in the mean times between rats and hamsters. - **Alternative Hypothesis (\(H_1\)):** Rats take more time on average than hamsters. 3. **Calculate the Test Statistic (\(t\)):** Compute the test statistic with precision up to three decimal places. 4. **Determine the P-value** Calculate the p-value, providing the result up to four decimal places. 5. **Compare P-value to \(\alpha\):** - Determine whether the p-value is less than or equal to \(\alpha\). 6. **Draw Conclusions:** - If the test results are statistically significant (\(p \leq \alpha\)), conclude there is sufficient evidence that rats take more time. - If not, conclude there is insufficient evidence. **Final Conclusion Options:** - The results indicate a significant difference at \(\alpha = 0.01\), allowing us to infer that rats take more time than hamsters. - The results are statistically insignificant, providing evidence that the times are equal. - The results are insignificant, indicating insufficient evidence for a difference in time. Complete the calculations and select the correct options based on your analysis results.
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