please show all work. I have provided tables and formula in the files
18. The average response time to a bank robbery is about 9 min. A local community wants to improve on this time, so they implement advanced training seminars. They find that the new response time for a sample of 35 police officers is 8 4.2 (MSD) min. Test whether this advanced training seminar reduced response time at a .05 level of significance. Show your work.
19.A researcher wants to determine the mean difference in productivity between employees working the morning shift (n = 16) and the night shift (n = 10). He finds that the sum of squares for the morning shift is 200 and the sum of squares is 500 for the night shift. What is the pooled variance? Show your work.
20. The mean crying time of a population of infants during naptime at a local preschool is 12 min. The school implements a new naptime routine in a sample of 25 infants and records an average crying time of 8 4.6 (MSD) min. Test whether this new naptime routine reduced crying time at a .05 level of significance. Show your work.
21. A professor teaches a certain section of material using a lot of examples with sports and cars to illustrate. He is concerned that this may have caused a difference in test scores between his male and female students. To test this, he measures exam grades from this section of material among women (n = 10) and men (n = 10). The mean score in the male group was 84 with a sum of squares of 144; in the female group, it was 78 with a sum of squares of 576 points. If the null hypothesis is that there is no difference in exam scores, then test the null hypothesis at a .05 level of significance for a two-tailed test. Show your work.
22. A nutrition store in the mall is selling Memory Booster, which is a concoction of herbs and minerals that is intended to improve memory performance. To test the effectiveness of the herbal mix, a researcher obtains a sample of 8 participants and asks each person to take the suggested dosage each day for 4 weeks. At the end of the 4-week period, each individual takes a standardized memory test. In the general population, the standardized test is known to have a mean of = 7.
Please show all of the steps of this hypothesis test to determine whether the Memory Booster concoction improves memory (including writing out the hypotheses). Please show ALL work. The data points are: 8, 9, 6, 8, 9, 8, 7, 9
