Espa An adventure company runs two obstacle courses, Fundash and Coolsprint. The designer of the courses suspects that the mean completion time of Fundash is not equal to the mean completion time of Coolsprint. To test this, she selects 200 Fundash runners and 255 Coolsprint runners. (Consider these as random samples of the Fundash and Coolspring runners.) The 200 Fundash runners complete the course with a mean time of 71.8 minutes and a standard deviation of 2.7 minutes. The 255 Coolsprint runners complete the course with a mean time of 71.2 minutes and a standard deviation of 2.6 minutes. Assume that the population standard deviations of the completion times can be estimated to be the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.10 level of significance, is there enough evidence to support the claim that the mean completion time, μ₁, of Fundash is not equal to the mean completion time, H₂, of Coolsprint? Perform a two-tailed test. Then complete the parts below. A Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.) D (a) State the null hypothesis Ho and the alternative hypothesis H₁. H P Ho :D H₁ : (b) Determine the type of test statistic to use. (Choose one) ▼ 0-0 0<0 (c) Find the value of the test statistic. (Round to three or more decimal places.) X Ś 0 (d) Find the two critical values at the 0.10 level of significance. (Round to three or more decimal places.) and (e) Can we support the claim that the mean completion time of Fundash is not equal to the mean completion time of Coolsprint? Yes No Explanation Check xl a 0=0 X S 7⁰ 00 P OSO 020 >D ? 00 A V
Espa An adventure company runs two obstacle courses, Fundash and Coolsprint. The designer of the courses suspects that the mean completion time of Fundash is not equal to the mean completion time of Coolsprint. To test this, she selects 200 Fundash runners and 255 Coolsprint runners. (Consider these as random samples of the Fundash and Coolspring runners.) The 200 Fundash runners complete the course with a mean time of 71.8 minutes and a standard deviation of 2.7 minutes. The 255 Coolsprint runners complete the course with a mean time of 71.2 minutes and a standard deviation of 2.6 minutes. Assume that the population standard deviations of the completion times can be estimated to be the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.10 level of significance, is there enough evidence to support the claim that the mean completion time, μ₁, of Fundash is not equal to the mean completion time, H₂, of Coolsprint? Perform a two-tailed test. Then complete the parts below. A Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.) D (a) State the null hypothesis Ho and the alternative hypothesis H₁. H P Ho :D H₁ : (b) Determine the type of test statistic to use. (Choose one) ▼ 0-0 0<0 (c) Find the value of the test statistic. (Round to three or more decimal places.) X Ś 0 (d) Find the two critical values at the 0.10 level of significance. (Round to three or more decimal places.) and (e) Can we support the claim that the mean completion time of Fundash is not equal to the mean completion time of Coolsprint? Yes No Explanation Check xl a 0=0 X S 7⁰ 00 P OSO 020 >D ? 00 A V
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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Transcribed Image Text:### Hypothesis Testing for Mean Completion Times
An adventure company operates two obstacle courses, Fundash and Coolsprint. The designer of the courses suspects that the mean completion time of Fundash is different from the mean completion time of Coolsprint. To test this hypothesis, random samples of 200 Fundash runners and 255 Coolsprint runners were selected. Here are the details of the analysis:
1. **Sample Information:**
- Fundash sample size ($n_1$): 200 runners
- Fundash mean completion time ($\bar{X}_1$): 71.8 minutes
- Fundash standard deviation ($S_1$): 2.7 minutes
- Coolsprint sample size ($n_2$): 255 runners
- Coolsprint mean completion time ($\bar{X}_2$): 71.2 minutes
- Coolsprint standard deviation ($S_2$): 2.6 minutes
2. **Hypotheses Formulation:**
- Null Hypothesis ($H_0$): The mean completion time of Fundash is equal to the mean completion time of Coolsprint ($\mu_1 = \mu_2$).
- Alternative Hypothesis ($H_1$): The mean completion time of Fundash is not equal to the mean completion time of Coolsprint ($\mu_1 \neq \mu_2$).
3. **Significance Level:**
- The test is conducted at a 0.10 level of significance.
4. **Test Statistic:**
- The type of test statistic to use needs to be determined based on the test's requirements (e.g., Z-test, t-test).
5. **Calculation and Analysis:**
- Compute the test statistic’s value (rounded to three or more decimal places).
- Determine the critical values at the 0.10 level of significance.
6. **Decision Making:**
- Based on the critical values and the computed test statistic, decide whether to reject or fail to reject the null hypothesis.
This framework will be used to test the hypothesis that the mean completion time of Fundash is not equal to the mean completion time of Coolsprint. The detailed steps will guide you through formulating hypotheses, choosing the correct statistical test, and making the final decision based on the calculated values.
Carry your intermediate computations to at least three decimal places for
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