One-sample t-test. A dietician is interested in observing if there is a relationship between caffeine intake from energy drink consumption and completing a specific cognitive task. He collects data to determine whether the amount of time to complete the cognitive task (µ= 5mins) is significantly different to the time it takes after drinking GFuel, an energy drink with a source of caffeine. Test with a = 0.05. Data: 3, 5, 4, 5, 4, 3 a. Conduct a complete hypothesis test b. Construct an 95% confidence interval c. Interpret your confidence interval d. Give a full APA-style write up of your results e. Do you have to consider a Type I error or a Type II error? Explain

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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.