An adventure company runs two obstacle courses, Fundash and Coolsprint, with similar designs. Since Fundash was built on rougher terrain, the designer of the courses suspects that the mean completion time of Fundash is greater than the mean completion time of Coolsprint. To test this, she selects 255 Fundash runners and 235 Coolsprint runners. (Consider these as independent random samples of the Fundash and Coolspring runners.) The 255 Fundash runners complete the course with a mean time of 77.6 minutes and a standard deviation of 8.6 minutes. The 235 individuals complete Coolsprint with a mean time of 76.0 minutes and a standard deviation of 7.6 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 0.05 level of significance, is there enough evidence to support the claim that the mean completion time, μ₁, of Fundash is greater than the mean completion time, μ₂, of Coolsprint? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. μ O P Ho :D H₁ :0 X S (b) Determine the type of test statistic to use. O=O OSO 20 (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) O 0 ? (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Can we support the claim that the mean completion time of Fundash is greater than the mean completion time of Coolsprint? Yes No X S
An adventure company runs two obstacle courses, Fundash and Coolsprint, with similar designs. Since Fundash was built on rougher terrain, the designer of the courses suspects that the mean completion time of Fundash is greater than the mean completion time of Coolsprint. To test this, she selects 255 Fundash runners and 235 Coolsprint runners. (Consider these as independent random samples of the Fundash and Coolspring runners.) The 255 Fundash runners complete the course with a mean time of 77.6 minutes and a standard deviation of 8.6 minutes. The 235 individuals complete Coolsprint with a mean time of 76.0 minutes and a standard deviation of 7.6 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 0.05 level of significance, is there enough evidence to support the claim that the mean completion time, μ₁, of Fundash is greater than the mean completion time, μ₂, of Coolsprint? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. μ O P Ho :D H₁ :0 X S (b) Determine the type of test statistic to use. O=O OSO 20 (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) O 0 ? (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Can we support the claim that the mean completion time of Fundash is greater than the mean completion time of Coolsprint? Yes No X S
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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![### Hypothesis Testing for Mean Completion Time
An adventure company runs two obstacle courses, Fundash and Coolsprint, with similar designs. Since Fundash was built on rougher terrain, the designer of the courses suspects that the mean completion time of Fundash is greater than the mean completion time of Coolsprint. To test this, she selects 255 Fundash runners and 235 Coolsprint runners.
(Consider these as independent random samples of the Fundash and Coolsprint runners.) The 255 Fundash runners complete the course with a mean time of 77.6 minutes and a standard deviation of 8.6 minutes. The 235 individuals complete Coolsprint with a mean time of 76.0 minutes and a standard deviation of 7.6 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 0.05 level of significance, is there enough evidence to support the claim that the mean completion time, μ₁, of Fundash is greater than the mean completion time, μ₂, of Coolsprint? Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.)
#### (a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \).
\[
H_0: \mu_1 \leq \mu_2
\]
\[
H_1: \mu_1 > \mu_2
\]
#### (b) Determine the type of test statistic to use.
- Options: z, t
#### (c) Find the value of the test statistic. (Round to three or more decimal places.)
\[
\text{Value of the test statistic: } [\quad]
\]
#### (d) Find the p-value. (Round to three or more decimal places.)
\[
\text{p-value: } [\quad]
\]
#### (e) Can we support the claim that the mean completion time of Fundash is greater than the mean completion time of Coolsprint?
- Yes
- No
---
### Additional Explanation
The image illustrates the steps required for a hypothesis testing scenario. The primary goal is to determine whether the mean completion time of one obstacle course (Fundash) is statistically](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd1b6d45-a7eb-422c-8cfa-b963b51ff783%2F004d35a4-97ea-4d62-92ff-1372ba45851c%2Fo3i3kji_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing for Mean Completion Time
An adventure company runs two obstacle courses, Fundash and Coolsprint, with similar designs. Since Fundash was built on rougher terrain, the designer of the courses suspects that the mean completion time of Fundash is greater than the mean completion time of Coolsprint. To test this, she selects 255 Fundash runners and 235 Coolsprint runners.
(Consider these as independent random samples of the Fundash and Coolsprint runners.) The 255 Fundash runners complete the course with a mean time of 77.6 minutes and a standard deviation of 8.6 minutes. The 235 individuals complete Coolsprint with a mean time of 76.0 minutes and a standard deviation of 7.6 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 0.05 level of significance, is there enough evidence to support the claim that the mean completion time, μ₁, of Fundash is greater than the mean completion time, μ₂, of Coolsprint? Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.)
#### (a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \).
\[
H_0: \mu_1 \leq \mu_2
\]
\[
H_1: \mu_1 > \mu_2
\]
#### (b) Determine the type of test statistic to use.
- Options: z, t
#### (c) Find the value of the test statistic. (Round to three or more decimal places.)
\[
\text{Value of the test statistic: } [\quad]
\]
#### (d) Find the p-value. (Round to three or more decimal places.)
\[
\text{p-value: } [\quad]
\]
#### (e) Can we support the claim that the mean completion time of Fundash is greater than the mean completion time of Coolsprint?
- Yes
- No
---
### Additional Explanation
The image illustrates the steps required for a hypothesis testing scenario. The primary goal is to determine whether the mean completion time of one obstacle course (Fundash) is statistically
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