A random-number generator is supposed to produce a sequence of Os and I s with each value being equally likely to be a 0 or a I and with all values being independent. In an examination of the random-number generator, a sequence of 50.000 values is obtained of which 25.264 are Os.
(a) Formulate a set of hypotheses to test whether there is any evidence that the random-number generator is producing Os and Is with unequal probabilities, and calculate the corresponding p-value.
(b) Compute a two-sided 99% confidence interval for the probability p that a value produced by the random-number generator is a 0.
(c) If a two-sided 99% confidence interval for this probability is required with a total length no larger than 0.005. How many additional values need to be investigated'.'