6. Two of the teams competing in the America's Cup are Team Oracle U.S.A. and Land Rover BAR. They race their yachts over a course several times. Below are a sample of times in minutes for each yacht. Assume the population standard deviations are the same. At the 0.05 significance level, can we conclude that there is a difference in mean times? Apply the 6-step hypothesis test procedure expressing your decision rule in both a) critical value terms and b) p-value terms. America's Cup Team Oracle Land Rover BAR 13.1 11.9 13.1 11.5 13.2 e10.0

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### Hypothesis Testing: America's Cup Yacht Race Analysis

In the America's Cup, two teams, Team Oracle U.S.A. and Land Rover BAR, compete by racing their yachts over a course multiple times. We're analyzing sample times in minutes for each yacht, assuming that the population standard deviations are equal.

#### Objective
Determine if there is a statistically significant difference in their mean times at a 0.05 significance level.

#### Methodology
Apply the 6-step hypothesis test procedure, and express the decision rule in terms of:
a) Critical value terms
b) P-value terms

#### Data Table
The table below shows the times recorded for each team:

| America's Cup       |            |          |
|---------------------|------------|----------|
| **Team Oracle**     | **Land Rover BAR** |
| 13.1                | 11.9       |
| 13.1                | 11.5       |
| 13.2                | 10.0       |
| 6.4                 | 12.3       |
| 14.8                | 10.2       |
| 15.7                | 10.4       |
| 15.1                | 10.6       |
| 14.3                | 12.3       |
| 12.4                | 14.2       |
| 12.6                | 13.3       |
| 9.8                 |            |
| 18.0                |            |

*You can copy and paste the numbers above directly into Microsoft Excel® for further analysis.*

This data will be used to perform t-tests to compare the mean times of the two teams and determine if there's a significant difference.
Transcribed Image Text:### Hypothesis Testing: America's Cup Yacht Race Analysis In the America's Cup, two teams, Team Oracle U.S.A. and Land Rover BAR, compete by racing their yachts over a course multiple times. We're analyzing sample times in minutes for each yacht, assuming that the population standard deviations are equal. #### Objective Determine if there is a statistically significant difference in their mean times at a 0.05 significance level. #### Methodology Apply the 6-step hypothesis test procedure, and express the decision rule in terms of: a) Critical value terms b) P-value terms #### Data Table The table below shows the times recorded for each team: | America's Cup | | | |---------------------|------------|----------| | **Team Oracle** | **Land Rover BAR** | | 13.1 | 11.9 | | 13.1 | 11.5 | | 13.2 | 10.0 | | 6.4 | 12.3 | | 14.8 | 10.2 | | 15.7 | 10.4 | | 15.1 | 10.6 | | 14.3 | 12.3 | | 12.4 | 14.2 | | 12.6 | 13.3 | | 9.8 | | | 18.0 | | *You can copy and paste the numbers above directly into Microsoft Excel® for further analysis.* This data will be used to perform t-tests to compare the mean times of the two teams and determine if there's a significant difference.
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