1.3 A random-number generator is supposed to produce a sequence of 0s and 1s with each value being equally likely to be a 0 or a 1 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 0 s. (a) Formulate a set of hypotheses to test whether there is any evidence that the random-number generator is producing 0s and 1s 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? 1.3 A random-number generator is supposed to produce a sequence of 0s and 1s with each value being equally likely to be a 0 or a 1 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 0 s. (a) Formulate a set of hypotheses to test whether there is any evidence that the random-number generator is producing 0s and 1s 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