Question 3 One pilot study estimated wheat price in July and in September using independent samples of wheat producers in the two months. Let X be the wheat price in September and Y the wheat price in July. Let # denote the true population mean wheat price in September and My the true population mean wheat price in July. Assume that the population variances of wheat prices in September and July are same. Consider the following statistics: Month Sample Size Sample Mean Sample SD September 36 $4.00 $0.20 July 26 $3.80 $0.30 a) (2 marks) Obtain the 95% confidence interval for the mean wheat price in September. b) (4 marks) Obtain the 90% confidence interval for the difference between the mean wheat prices in September and July. c) (4 marks) Economic researchers believe that, on average, the wheat price in September increases by less than $0.30 compared to July. Conduct a hypothesis test on such a statement at a significance level 0.01