Problem 6: Type 1 / Type 2 error Refer to the conclusion from Problem 5. Based on the conclusion (reject the null or fail to reject the null), what type of error {either Type 1 or type 2) could you have made? Explain. Problem 7: Study time 3 Use R. command t .test() to repeat Problem 5. (Test whether students who plan to go to graduate school study more than students who don't at o' = 0.1). Copy and paste your R. command and output. Note to students : R uses \"'Weleh's degrees of freedom\" instead of minimum of n1 1, Hz 1, hence gives a slightly different pvalue from Problem 5. Problem 8: Multiple choice Pvalue of hypothesis test Ha : n, = n2 is 0.03. Which of the following is always true? Explain, (A) Using the same sample information, the 95% condence interval for #1 #2 will contain 0. B Using the same sample information, the 99% condence interval for p. it will contain 0. 1 2 (C) Using the same sample information, the 95% confidence interval for p51 #2 will contain positive numbers only