Q2. A random sample of 64 observations produced the following summary statistics: the sample mean 78.2 and sample standard deviation 50. (a) Test the null hypothesis that = 90 against the alternative hypothesis that < 90, using = 0.05. (b) Test the null hypothesis that = 90 against the alternative hypothesis that 6= 90, using = 0.05. Interpret the result. (c) Find the pvalue for each test.