- Suppose the random variable X, the inner diameter of a steel tube, is normally distributed with σ =0.02 in. A random sample of 25 tubes had a sample mean, X = 2.41 in. a) Using a significant level of 0.05, is there enough evidence to reject Ho: μ-2.40 in favor of Hi: μ>2.40? b) For a), rather than a hypothesis test, the inference objective was a 98% confidence interval on μ. How large a sample of tubes would be needed for to be within 0.005 in. of u?