The average final exam score for the statistics course is 78%. A professor wants to see if the average final exam score for students who are given colored pens on the first day of class is lower. The final exam scores for the 12 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal. 87, 61, 89, 54, 69, 60, 54, 70, 68, 54, 84, 81 What can be concluded at the the ax = 0.05 level of significance level of significance? a. For this study, we should use t-test for a population mean b. The null and alternative hypotheses would be: Hou Select an answer H₁: Select an answer c. The test statistic ? d. The p-value = a e. The p-value is ? v f. Based on this, we should g. Thus, the final conclusion is that ... = (please show your answer to 3 decimal places.) (Please show your answer to 4 decimal places.) Select an answer the null hypothesis. The data suggest the population mean is not significantly lower than 78 at a = 0.05, so there is statistically insignificant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is equal to 78. O The data suggest the populaton mean is significantly lower than 78 at x = 0.05, so there is statistically significant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is lower than 78. O The data suggest that the population mean final exam score for students who are given colored pens at the beginning of class is not significantly lower than 78 at a = 0.05, so there is statistically insignificant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is lower than 78.