8. How does the shape of a t distribution compare with the normal distribution? How does the shape of a t distribution depend on sample size (n)? 9. A nutrition store in the mall is selling Memory Booster which is a concoction of herbs and minerals that is intended impact memory performance. To test the effectiveness of the herbal mix, a researcher obtains a sample of n = 16 people and asks each person to take the suggested dosage each day for 4 weeks. At the end of the four-week period, each individual takes a standardized memory test. The scores from the sample produced a mean of M = 26 with SS = 960. In the general population, the standardized test is known to have a mean of u = 20. Does the Memory Booster have a significant effect on memory performance? a. What is the null hypothesis (in words) (1-point)? b. What is the alternative hypothesis (in words) (1-point)? c. What is the t-obtained value (obtained t-statistic)? (3-points) d. Do you reject or fail to reject the null hypothesis? (1-point) e. What type of error might you be making? (1-point)_ f. Based on your findings, what would you conclude (be specific and relate back to question)? (2-points)_ 10. The number of dates the men's dorm of "Tranquility House" was pathetically low. Boredom got the best of Jason Rompacabeza one long, lonely Friday night, so he decided to take a poll of 30 of his fellow dorm-mates regarding the number of dates each had during the past month. The average number of dates was 2.2, with a standard deviation of . 65. He knew from a report recently published by the university that the average number of dates for all other dorm-dwellers was 4.6 dates per month. Are the men of Tranquility House significantly less likely to go out on dates than others living in dorms at the university? a. What is the null hypothesis (in words) (1-point)? b. What is the alternative hypothesis (in words) (1-point)? . What is the t-obtained value (obtained t-statistic)? (3-points) d. Do you reject or fail to reject the null hypothesis? (1-point)_ e. Based on your findings, what would you conclude (be specific and relate back to question)? (2-points)_