Valeria thinks that she has a special relationship with the number 5. In particular, Valeria thinks that she would roll a 5 with a fair 6-sided die more often than you'd expect by chance alone. Suppose pis the true proportion of the time Valena will roll a 5. (a) State the null and altemative hypotheses for testing Valeria's claim. (Type the symbol "p" for the population proportion, whichever symbols you need of "<", ">", "=", "not =" and express any values as a fraction eg p= 1/3) Ho = H = (b) Now suppose Valeria makes n= 46 rolls, and a 5 comes up 10 times out of the 46 rolls. Detemine the P-value of the test, giving your answer to 4 decimal places. Please use 3 decimal places in your test statistic when finding the P-value P-value = (C) Answer the question. Does this sample provide evidence at the 5 percent level that Valeria rolls a 5 more often than you'd expect? (Type: Yes or No)

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Part I: Probability For each of the following problems, you should write your answer as an expression. Do not give the final numeric value. For example, you should write C(4,2)/24 instead of 0.375. 5. You are playing Scrabble and you draw seven tiles: M, A, T, C, H, E, S. You line them up in some random order on your tile rack (assume all orderings are equally likely). The events M, T, and S are defined as follows: M: The tiles M, A, T, H appear consecutively. T: The tile T appears exactly in the middle (fourth position). S: The tile S is either in the first position or in the final position. Calculate the probability of each event; that is, p(M), p(T), and p(S). 5.1 5.2 What is p(MIT)? 5.3 What is p(MIS)? 5.4 5.5 What is p(T|S)? Consider all pairs of events: (M,T), (M,S), and (T,S). Which pairs of events are independent and which pairs of events are not independent? Justify your answer.

Let p be the population proportion of​ successes, where a success is an adult in the country who would travel into space on a commercial flight if they could afford it. State H0 and Ha. Select the correct choice below and fill in the answer boxes to complete your choice. ​(Round to two decimal places as​ needed.)

Suppose you are conducting a test of significance to try to determine whether your cat, Hope, will go to the correct object (out of two) when it is pointed to. You test Hope 100 times and finds she goes to the correct object in 70 out of those 100 trials. In this scenario, what is the variable? Whether or not Hope goes to the correct object The 100 trials The proportion of the 100 trials that Hope goes to the correct object The long term proportion (probability) that Hope will go to the correct object

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Last year the average math SAT score for students at one school was 775. the Headmaster introduced new methods hoping to improve scores. this year , the math mean SAT score for a sample of students was 1178. If the teaching had no effect, there would be roughly a 3 in 100 chance of seeing such an increase. Does the result have STATISTICAL significance? does the result have PRACTICAL significance? exlain your answer

Let's calculate the probability of finding someone special. Using a form of Fermi's Paradox (the difference between having limited or no choices to having high amount of choices). Let's calculate your probability using the following data. Multiply the number and all percentages together N (subscript p): Number of people = your target population (number of people in your state). Broward County, FL is 1,953, 251 million. Dade County, FL is 2,717,251 million. Palm Beach County, FL is 1, 497,251 million. Harris County, TX is 4,731,251 million. (example: 1,374,251 x .5 x .44 x .37 x .25 x.10 x.10 = 279 people are potential special people for you) times f (subscript g) = target gender (multiply as a decimal. Example: 0.5 for either sex or 1.0 for both sexes) times f (subscripts) = single people (multiply as a decimal) About 44% of people are single at any given time. f (subscript e) = the number of people you'll run into (multiply as a decimal). Your sample size will be small if you only…

"A manufacturer of shampoo claims that 72% of the shampoo users prefer brand X. To test this claim, a random sample of 44 participants are selected and asked what brand they prefer. If 31 of the 44 participants prefer brand X, what conclusion do we draw? Use a 0.1 level of significance. What are the given? hypothesized proportion:Blank 1% sample proportion:Blank 2 (Write your answer in fraction form form and simplify your answer) sample size:Blank 3 level of significance:Blank 4 What are the critical values? Write the positve first then the negative z:Blank 5 andBlank 6 What is the calculated z? Round your answer to the nearest hundredths. z:Blank 7"