Frogs have been breeding like flies at the Enormous State University (ESU) campus! Each year, the pledge class of the Epsilon Delta fraternity is instructed to tag all the frogs residing on the ESU campus. Two years ago (t = 0) they managed to tag all 42,000 of them (with little Epsilon Delta Fraternity tags). This year's pledge class discovered that all the tags had fallen off, and they wound up tagging a total of 63,000 frogs. (a) Find an exponential model for the frog population. f(t) =

A shoe company wants to determine if the new tread on its top line of running shoes lasts longer than the original tread. The company recruits 50 runners for a study. Each runner will perform their typical workout wearing one shoe with the original tread on one foot and another shoe with the new tread on the other foot. The foot that wears the new type of tread will be decided by flipping a coin. After one month, the runner will wear the new type of tread on the opposite foot. At the end of the second month, the difference in tread wear (New – Original) will be calculated. What type of sampling is described in this study? What is the appropriate inference procedure? one-sample t-test for  one-sample z-test for p one-sample t-test for  two-sample t-test for

Mateo believes that completely cutting caffeine out of a person's diet will allow them more restful sleep at night. He randomly selects 8 adults to help him test this theory. Each person is asked to consume two caffeinated beverages per day for 28 days and then cut back to no caffeinated bevarages for an additional 28 days. During each period, the participants record the number of nights of restful sleep that they had. The following table gives the results of the study. Test Mateo's claim at the 0.05 level of significance. Give answers to 4 decimal places as needed. Number of Nights of Restful Sleep in a Four-Week Period 15 With Caffeine 21 20 22 24 18 21 24 20 26 26 22 21 23 27 23 Without Caffeine a) The normal probability plot showed the differences follow a normal distribution and the boxplot showed no outliers. b) Test the claim (1) Determine the null and alternative hypotheses. Enter correct symbol and values Ho: H₁: (2) Type of test: (3) a = (4) Test statistic (to) = p-value =…

For the remainder of this question, we will consider one of the world's most popular video games, Minecraft (adapted from Mills & Mills, 2016). In this game, the character (you) can attempt to tame a wolf with a bone. Assume that you get 9 tries to tame the wolf, i.e. there are 9 bones. Each time you tame the wolf, the wolf becomes a dog and a new wolf appears which you can then attempt to also tame. This continues until you have used up all 9 bones, and the goal is to end up with as many dogs as possible at the end of the game. The probability of taming the wolf with each attempt is fixed at 0.54. Let X denote the number of dogs at the end of the game so that X~ BIN (9,0.54). Assume you are about to play the game. 15. The probability that you will tame some number a or less dogs is 0.66144. What must be (round to the nearest whole number)?

You randomly recruit 23 students and tell each of them to come to the lab in two different mornings: each morning they will be offered some breakfast and will take a test. Each student will receive the light breakfast one time and the nutritious breakfast the other time (some will receive the light breakfast first, the others will receive the nutritious breakfast first, and the second time they switch). The average difference in a student’s score after eating the nutritious breakfast and their score after eating a light breakfast is 4.5, and the standard deviation of this difference is 3.6. (a)  Construct a 95% confidence interval for the difference in the average score of students after having a nutritious breakfast and the average score of students after having a light breakfast.

A teacher was listening to some of her students talk about how many SnapChats they send during the day. The teacher decided that she wanted to conduct a study to see if the number of SnapChats a student sends per day affects how much time students talk to their friends face-to-face. So, the teacher let her 2nd period class continue sending Snaps as they always have. Then, the teacher told her 5th period that they were to not watch use SnapChat for a whole day. Then, the teacher had students record how many conversations they had with their friends during the week, gathered the data, and analyzed the results. c. What was the research question?