statistics

A researcher is testing the hypothesis that consuming a sports drink during exercise improves endurance. A sample of n=50 male college students is obtained and each student is given a series of three endurance tasks and asked to consume 4 ounces of the drink during each break between tasks. The overall endurance score for this sample is M=53. For the general population, without any sports drink, the scores for this task average m=50 with a standard deviation of σ=12.
a. Can the researcher conclude that endurance scores with the sports drink are significantly higher than scores without the drink? Use a one- tailed test with α=.05.
b. Can the researcher conclude that endurance scores with the sports drink are significantly different than scores without the drink? Use a two- tailed test with α=.05.
c. You should find that the two tests lead to different conclusions. Explain why.

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  1. Briefly explain how increasing sample size influences each of the following. Assume that all other factors are held constant.
    a. The size of the z- score in a hypothesis test.
    b. The size of Cohen’s d.
    c. The power of a hypothesis test.

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