For a random sample of 12 students, the sample mean time to complete a particular stat 420 homework assignment was 97 minutes with sample standard deviation of 13.5 minutes. assume that the time to complete this assignment is normally distributed. a certain stat 420 instructor claims that the average time to complete this assignment is at most 90 minutes. test h0 : μ < 90 vs h1 : μ > 90 at a 10% significance level. find
(i) the value of the test statistic;
(ii) the critical value(s) at a=0.10 level of significance;
(iii) the p-value (approximately) for this test;
(iv) the decision at a = 0.10 level of significance.