1) 2) Research has indicated that most 3-year-olds should sleep about 11 hours a day. I think that this number might be different. To test this, I recruit 6 children who are 3-years-old to be in my study. Their guardians were instructed to keep track of how much daily sleep their infants got over the next 30 days. After 30 days the following average daily sleep totals were: 12,12, 11, 11,13,14. State the research hypothesis, and the null hypothesis in words. No notation needed. Is the research hypothesis a one-tailed (directional) or two-tailed (non-directional) hypothesis? How do you know? Using what you know from the information listed in the problem, what type of t-test would you conduct paired samples (dependent) or one sample (single)? Provide a brief rationale for your choice. Now perform the necessary calculations (i.e., conduct the appropriate t-test). Make sure you show your hand calculations here in order to receive credit. In the lectures this week, I walk you through how to calculate both types of t-tests. Make sure you show all of those steps mentioned in those lectures. Using the .05 signicance level (test the appropriate direction as noted in the research hypothesis), what can we conclude about the prediction that 3-year-olds will sleep for 11 hours a day? I would like you to provide the answer to this question in two ways: (hint: see lecture for these) - Provide your answer in a way that someone who has never taken statistics would understand. ' Provide your answer in APA style There is a lot of talk about whether the pandemic has signicantly increased the prices of groceries. I wanted to see if this was the case for milk prices. I located the average whole milk prices from 6 cities pre-pandemic and during the pandemic. Their information is below. Cites February 2019 February 2021 Atlanta GA 3.36 3.61 Baltimore, MD 3.70 3.98 Boston, MA 3.23 353 Chicago, IL 3.99 4.16 Cincinnati, OH 2.26 2.87 Dallas, TX 2.42 2.92 State the research hypothesis, and the null hypothesis. Is the research hypothesis a one-tailed (directional) or two-tailed (non-directional) hypothesis? How do you know? Using what you know from the information listed in the problem, what type of ttest would you conduct paired samples (dependent) or one sample (single)? Provide a brief rationale for your choice New perform the necessary calculations (i.e., conduct the appropriate t-test). Make sure you Show your hand calculations here in order to receive credit. In the lectures this week, I walk you through how to calculate both types of t-tests. Make sure you show all of those steps mentioned in those lectures. Using the .05 signicance level (test the appropriate direction as noted in the research hypothesis), what can we conclude about the prices of whole milk? I would like you to provide the answer to this question in two ways: (hint: see lecture for these) Introduction to Statistics Homework: Single and Paired T-Tests - Provide your answer in a way that someone Who has never taken statistics would understand. a Provide your answer in APA style