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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 230 Fundash runners and 275 Coolsprint runners. (Consider these as independent random samples of the Fundash and Coolspring runners.) The 230 Fundash runners complete the course with a mean time of 78.5 minutes and a standard deviation of 8.1 minutes. The 275 individuals complete Coolsprint with a mean time of 76.7 minutes and a standard deviation of 6.5 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 0.01 level of significance, is there enough evidence to support the claim that the mean completion time, ₁, of Fundash is greater than the mean completion time, H₂ 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. Ho H₁ :0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) (e) Can we support the claim that the mean completion time of Fundash is greater than the mean completion time of Coolsprint? OYes No μ X 4 a S X 2 On ロ=ロ OSO ☐☐ OO

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 230 Fundash runners and 275 Coolsprint runners. (Consider these as independent random samples of the Fundash and Coolspring runners.) The 230 Fundash runners complete the course with a mean time of 78.5 minutes and a standard deviation of 8.1 minutes. The 275 individuals complete Coolsprint with a mean time of 76.7 minutes and a standard deviation of 6.5 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 0.01 level of significance, is there enough evidence to support the claim that the mean completion time, ₁, of Fundash is greater than the mean completion time, H₂ 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. Ho H₁ :0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) (e) Can we support the claim that the mean completion time of Fundash is greater than the mean completion time of Coolsprint? OYes No μ X 4 a S X 2 On ロ=ロ OSO ☐☐ OO

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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SLICE NAME Confidence Intervals and Hypothesis Testing TOPIC NAME Hypothesis test for the difference of population means: Z test
Done O CONFIDENCE INTERVALS AND HYPOTHESIS... Hypothesis test for the difference... O▬▬0 www-awu.aleks.com (a) State the null hypothesis Ho and the alternative hypothesis H₁. HO H₁:0 (b Determine the pe of test statistic to use. (Choose one) ▼ (c) Fit Español An adventure company runs two obstacle courses, Fundash and Co with similar designs. Since Fundash was built on rougher terrain, th designer of the courses suspects that the mean completion time of is greater than the mean completion time of Coolsprint. To test this selects 230 Fundash runners and 275 Coolsprint runners. (Consider th independent random samples of the Fundash and Coolspring runne 230 Fundash runners complete the course with a mean time of 75 m and a standard deviation of 8.1 minutes. The 275 individuals complete Coolsprint with a mean time of 76.7 minutes and a standard deviatio minutes. Assume that the population standard deviations of the com times can be estimated to be the sample standard deviations, since samples that are used to compute them are quite large. At the 0.01 significance, is there enough evidence to support the claim that the completion time, ₁, of Fundash is greater than the mean completio 12 of Coolsprint? Perform a one-tailed test. Then complete the part Chi-Square Carry your intermediate computations to at least three decimal pla necessary, consult a list of formulas.) F (d) and the p-value Round to three or more decimal places.) ☐ Explanation 0/5 0/5 tes statistic. (Round to three or more decimal places.) (e) Can we support the claim that the mean completion time of Fundash is greater than the mean completion time of Coolsprint? OYes No Check AA Evelyn V μ X 89 ローロ O#O X O S 0₂ OSO O<O C © 2023 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center
Transcribed Image Text:Done O CONFIDENCE INTERVALS AND HYPOTHESIS... Hypothesis test for the difference... O▬▬0 www-awu.aleks.com (a) State the null hypothesis Ho and the alternative hypothesis H₁. HO H₁:0 (b Determine the pe of test statistic to use. (Choose one) ▼ (c) Fit Español An adventure company runs two obstacle courses, Fundash and Co with similar designs. Since Fundash was built on rougher terrain, th designer of the courses suspects that the mean completion time of is greater than the mean completion time of Coolsprint. To test this selects 230 Fundash runners and 275 Coolsprint runners. (Consider th independent random samples of the Fundash and Coolspring runne 230 Fundash runners complete the course with a mean time of 75 m and a standard deviation of 8.1 minutes. The 275 individuals complete Coolsprint with a mean time of 76.7 minutes and a standard deviatio minutes. Assume that the population standard deviations of the com times can be estimated to be the sample standard deviations, since samples that are used to compute them are quite large. At the 0.01 significance, is there enough evidence to support the claim that the completion time, ₁, of Fundash is greater than the mean completio 12 of Coolsprint? Perform a one-tailed test. Then complete the part Chi-Square Carry your intermediate computations to at least three decimal pla necessary, consult a list of formulas.) F (d) and the p-value Round to three or more decimal places.) ☐ Explanation 0/5 0/5 tes statistic. (Round to three or more decimal places.) (e) Can we support the claim that the mean completion time of Fundash is greater than the mean completion time of Coolsprint? OYes No Check AA Evelyn V μ X 89 ローロ O#O X O S 0₂ OSO O<O C © 2023 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center
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 230 Fundash runners and 275 Coolsprint runners. (Consider these as independent random samples of the Fundash and Coolspring runners.) The 230 Fundash runners complete the course with a mean time of 78.5 minutes and a standard deviation of 8.1 minutes. The 275 individuals complete Coolsprint with a mean time of 76.7 minutes and a standard deviation of 6.5 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 0.01 level of significance, is there enough evidence to support the claim that the mean completion time, ₁, of Fundash is greater than the mean completion time, H₂, 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. HO H₁:0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) Espanol (d) Find the p-value. (Round to three or more decimal places.) (e) Can we support the claim that the mean completion time of Fundash is greater than the mean completion time of Coolsprint? OYes O No H X ■ a S X 2 0#0 O<O Р ê ロ=ロ OSO 020 S Olo 0 O>0
Transcribed Image Text: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 230 Fundash runners and 275 Coolsprint runners. (Consider these as independent random samples of the Fundash and Coolspring runners.) The 230 Fundash runners complete the course with a mean time of 78.5 minutes and a standard deviation of 8.1 minutes. The 275 individuals complete Coolsprint with a mean time of 76.7 minutes and a standard deviation of 6.5 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 0.01 level of significance, is there enough evidence to support the claim that the mean completion time, ₁, of Fundash is greater than the mean completion time, H₂, 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. HO H₁:0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) Espanol (d) Find the p-value. (Round to three or more decimal places.) (e) Can we support the claim that the mean completion time of Fundash is greater than the mean completion time of Coolsprint? OYes O No H X ■ a S X 2 0#0 O<O Р ê ロ=ロ OSO 020 S Olo 0 O>0
Expert Solution
Step 1

The question is about hypo. testing

Given :

Randomly selected no. of runners of course " F " ( n1 ) = 230

Randomly selected no. of runners of course " C " ( n2 ) = 275

Sample mean completion time of " F " runners ( x¯1 ) = 78.5 min.

Sample mean completion time of " C " runners ( x¯2 ) = 76.7 min.

Popl. std. deviation estimated to be sample std. deviation

Std. deviation of completion time of " F " runners ( σ1 ) = 8.1 min.

Std. deviation of completion time of " C " runners ( σ2 ) = 6.5 min.

Level of signif. ( α ) = 0.01

 

To find : 

Is there any evid. that mean completion time of " F " runners is greater than mean completion time of " C " runners

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