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# Consider a set of N=30 random numbers generated by a (six-sided) die:

INSTRUCTIONS TO CANDIDATES

Exercise Statistical Testing

Consider a set of N=30 random numbers generated by a (six-sided) die:

2 3 3 4 4 3 3 3 3 5 3 1 6 3 3 4 6 1 1 2 5 6 6 3 1 6 3 2 3 3

1. Assuming an ideal die that generates scores of One, Two, Three, Four, Five and Six with equal probability 1/6, what is that ideal die's mean scoreμ?

2. What is the mean of the numbers in the set above? And what is the standard deviations of the numbers (using N-1 degrees of freedom); and from this, what is the standard error, SE(x), of the mean?

Now the central question of this exercise: Does differ significantly from the mean of the ideal die? Or in other words, is the difference significantly non-zero (this is the same as in the lecture except that here you are not interested in the difference between the means of two sets of numbers but in the difference between the mean of a set of numbers (x) and some constant number (u)). To answer this question, proceed as described in the lecture:

a. Define the null hypothesis and the alternative hypothesis (analogous to the lecture).

b. Calculate your t-statistic t, analogous to the lecture, from the quantities, μs and N. Here use that the standard deviation of is naturally zero (because it is a "natural" constant derived from probability theory), so the standard error SE() just equals SE() which you calculated above.

c. Calculate the null sampling distribution of your test-statistic, i.e. the distribution f(t) of t-values that you obtain given your null hypothesis is true. For this use the formula from the lecture

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