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*Today we are going to come up with new task, that is about ”Show all your work. Indicate clearly the methods you use, because you will be scored on…“. We have found the solution to this question, along with interesting information related to it, thanks to its novelty and interest. This will help you to develop a more research-oriented mindset, and make it easier for you to answer these types of questions. This is where we will focus to gain this useful and new knowledge!*

## Question: “Show all your work. Indicate clearly the methods you use, because you will be scored on…”

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Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations.

A team of psychologists studied the concept of visualization in basketball, where players visualize making a basket before shooting the ball. They conducted an experiment in which 20 basketball players with similar abilities were randomly assigned to two groups. The 10 players in group 1 received visualization training, and the 10 players in group 2 did not.

Each player stood 22 feet from the basket at the same location on the basketball court. Each player was then instructed to attempt to make the basket until two consecutive baskets were made. The players who received visualization training were instructed to use visualization techniques before attempting to make the basket. The total number of attempts, including the last two attempts, were recorded for each player.

The total number of attempts for each of the 20 players are summarized in the following boxplots.

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(a) Based on the boxplots, did basketball players who received visualization training tend to need fewer attempts to make two consecutive baskets from a distance of 22 feet than players who did not receive the training? Explain your reasoning.

(b) State and check conditions for conducting a two-sample t-test for a difference in means.

Because both distributions, visualization (V) and no visualization (NV), are skewed, the psychologists conducted a simulation to test for a difference in medians rather than means. For each trial of the simulation, the 20 values of the total number of attempts observed in the experiment were combined into one group and then randomly split into two groups of 10. The difference in the medians (V-NV) of the groups was calculated for each trial. The following dot plot shows the difference in the medians for 100 trials of the simulation.

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(c) Using the observed difference in medians (V-NV) and the results of the simulation, estimate a p-value for a test for the difference in medians. Show the work needed to calculate this p-value.

(d) Based on the p-value in part (c), is there convincing statistical evidence that basketball players similar to the ones in this study who receive visualization training need fewer attempts to make two consecutive baskets from a distance of 22 feet than those who do not receive such training? Justify your answer.

## Answer

a) Based on the boxplot Q1, Q2 and Q3 of visualization is smaller than the corresponding Q1 ,O2 and Q3 of no visualization except one outlier observation on the visualization group. Hence, basketball players who received visualization training group tend to nad fewer attempts to make two consecutive baskets from a distance of 22 feet than players who did not received the training

b, The assumption of a tworsample t-test for a difference in means that both the sample are draw out randoruly and folloin the normal distribution. The visualization data set include a outlier observation and non-visualization data set is a positively skewed… Hence, the assumption or normality on both the samples are violated. Hence, two-sample to test for a difference in means is not a appropriate test statistic in this data,

c, Median ( U-MV) = 4-7=-3

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d) P-value =0,23 is greater than 0.05 level of significance, Hence, there is no convincing statistical evidence that basketball players similar to the ons in the study who receive visualization training need fewes attempts to make two consecutive baskets hom a distance of 22 feet than those who do not recure such training.

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## Relevant knowledge

To obtain the volume of the bound region after the revolution of the region around a given axis, the definite integral must be used in continuous functions of many types. To get the volume integral, you can use either the washer or shell method.

## Conclusion

*This is how you solve this type of task “ Show all your work. Indicate clearly the methods you use, because you will be scored on…”. Please leave a message below if you have any questions or comments.*

*Thanks for reading!!!*

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