Question 5: A machine is set up such that the average content of juice per bottle equals p. A sample of 100 bottles yields an average content of 48cl. Assume that the population standard deviation is 5cl. a) Calculate a 90% and a 95% confidence interval for the average content. b) What sample size is required to estimate the average contents to within 0.5cl at the 95% confidence level? Suppose that, instead of 100 bottles, 36 bottles were sampled instead. The sample of 36 bottles yields an average content of 48.5cl. a) Test the hypothesis that the average content per bottle is 50cl at the 5% significance level. b) Can you reject the hypothesis that the average content per bottle is less than or equal to 45cl, using the same significance level as in part (a)?