Hi, I need help with these questions. Thank you.

The average final exam score for the statistics course is 81%. 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 15 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal. 86, 91, 56, 80, 91, 71, 79, 65, 91, 79, 68, 69, 78, 92, 71 What can be concluded at the the a = 0.05 level of significance level of significance? a. For this study, we should use b. The null and alternative hypotheses would be: E-CZ) (Round intermediate values to 2 decimal places. Please show your c. The test statistic ? answer to 3 decimal places.) Currently patrons at the library speak at an average Of 61 decibels. Will this average increase after the installation of a new computer plug in station? After the plug in station was built, the librarian randomly recorded 70 people speaking at the library. Their average decibel level was 61.6 and their standard deviation was 6. What can be concluded at the the a = 0.10 level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: C d. The p-value = places. ) (Using your rounded test statistic, please show your answer to 4 decimal e. The p-value is a f. Based on this, we should the null hypothesis. g. Thus, the final conclusion is that O The data suggest the populaton mean is significantly lower than 81 at a = 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 81. O The data suggest the population mean is not significantly lower than 81 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 81. 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 81 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 81. Nationally, patients who go to the emergency room wait an average of 4 hours to be admitted into thee hospital. Do patients at rural hospitals have a higher waiting time? The 11 randomly selected patients who went to the emergency room at rural hospitals waited an average of 5.6 hours to be admitted into the hospital. The standard deviation for these 11 patients was 2.9 hours. What can be concluded at the the a = 0.05 level of significance level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: (please show your answer to 3 decimal places.) c. The test statistic ? = c. The test statistic (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places. ) e. The p-value is a f. Based on this, we should the null hypothesis. g. Thus, the final conclusion is that O The data suggest the populaton mean has significantly increased from 61 at a = O. 10, so there is statistically significant evidence to conclude that the population mean decibel level at the library has increased since the plug in station was built. O The data suggest the population mean has not significantly increased from 61 at a = O. 10, so there is statistically significant evidence to conclude that the population mean decibel level at the library has not increased since the plug in station was built. O The data suggest that the population mean decibal level has not significantly increased from 61 at a O. 10, so there is statistically insignificant evidence to conclude that the population mean decibel level at the library has increased since the plug in station was built. d. The p-value = (Please show your answer to 4 decimal places.) e. The p-value is a f. Based on this, we should the null hypothesis. g. Thus, the final conclusion is that O The data suggest the population mean iS not significantly higher than 4 at a - 0.05, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is equal to 4 hours. O The data suggest the populaton mean is significantly higher than 4 at a = 0.05, so there is statistically significant evidence to conclude that the population mean waiting time to be a