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. A study was conducted by researchers for a top European soccer club to investigate the relationship between the air pressure in a soccer ball and the maximum speed that players can kick the ball. Two soccer balls of the same size and type were used for the experiment. One soccer ball was filled to 8.5 pounds per square inch (psi) and the other was filled to 15.6 psi, the minimum and maximum recommended air pressures for the type of training ball used by the club. Each player at a training session one day kicked the ball filled to 8.5 psi and the ball filled to 15.6 psi, and the maximum speeds in miles per hour (mph) at which the balls traveled were recorded. The order in which the two soccer balls were kicked was randomly assigned, and the players did not have any knowledge about what data were being recorded nor the air pressures in the soccer balls. What type of study design was used by the researchers and which of the following confidence interval procedures would be most appropriate for these data, assuming that the conditions for inference are met? (A) A matched-pairs design and a one-sample t-interval for a mean difference (B) A matched-pairs design and a two-sample t-interval for a difference between two means (C) A completely randomized design and a one-sample t-interval for a mean difference (D) A completely randomized design and a two-sample t-interval for a difference between two means (E) An observational study and a confidence interval procedure would not be appropriate Inauthorized

Question

. A study was conducted by researchers for a top European soccer club to investigate the relationship between the air pressure in a soccer ball and the maximum speed that players can kick the ball. Two soccer balls of the same size and type were used for the experiment. One soccer ball was filled to 8.5 pounds per square inch (psi) and the other was filled to 15.6 psi, the minimum and maximum recommended air pressures for the type of training ball used by the club. Each player at a training session one day kicked the ball filled to 8.5 psi and the ball filled to 15.6 psi, and the maximum speeds in miles per hour (mph) at which the balls traveled were recorded. The order in which the two soccer balls were kicked was randomly assigned, and the players did not have any knowledge about what data were being recorded nor the air pressures in the soccer balls. What type of study design was used by the researchers and which of the following confidence interval procedures would be most appropriate for these data, assuming that the conditions for inference are met? (A) A matched-pairs design and a one-sample t-interval for a mean difference (B) A matched-pairs design and a two-sample t-interval for a difference between two means (C) A completely randomized design and a one-sample t-interval for a mean difference (D) A completely randomized design and a two-sample t-interval for a difference between two means (E) An observational study and a confidence interval procedure would not be appropriate Inauthorized

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Solution

The study design used by the researchers is a matched-pairs design. This is because each player kicked both balls, and the results from the two kicks by the same player are naturally paired. The most appropriate confidence interval procedure for these data, assuming that the conditions for inference are met, would be a one-sample t-interval for a mean difference. This is because we are interested in the mean difference in the maximum speeds of the two balls for each player, not the difference between two separate means. Therefore, the answer is (A) A matched-pairs design and a one-sample t-interval for a mean difference.

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