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1. Boxes cerval net weight ounces The veights assumed normally distributed. new cereal ispurchased andwe wishtol thato average. puts Aleast correct amount ofecreal boxes We randomly select 6 boxes, and find they have weights with sample mean 8.10 sample standard deviation 20ounces. (a) Suppose your data included all the box weights How would you check the normal distribution Explain what would indicate violation this as sumption (Note: You not have perform the check the given data. (b) Perform test hypothesis that the average net weight of cereal produced by hinei Sounces against the alternative that greater than Sounces Test level a 0.05 (Clearly define paramete you're estimating and the hypotheses you retesting, and give full and 2. Totest whether friend's Googly powers. display two windows entered either "Left' "Right depending which way Googly facing Then the random number generator selected either left window, withprobability 0.5 for which display star. Let probability Googly guesses correctly given (assume this sonstant In 80 trials correctly guessed window withthe star Itimes (a) Using nathematical notation, write down and alternative hypotheses for one- sided test. (b) If the test statistic the number guesses trials, write down codeto find the P-value ofs one-sided test (c) Even without that Googly's success rate sexpected ralue under "-value State your about fish's psychic powers. (d) Continued from (b). Ifyou only that the code dbinom(40, 80, 0.5) gives nember 0889. how would exact P-value (thetest (Hint: usethe property of a symmetric probabilty distribution.) 3. The file snoqualmie14 txt contains the daily precipitation (in Snoqualmie Falls, WA fora random 365 days. After oyour computer you canload it intol entering the command: rainfall scan(file .choose()) d then seleeting (a) Show that data does not come from normally distributed population Include graph support your answer (b) The mean annual rainfall Seattle is 37. inches per year. Test (at level 0.05) the hypothesis mean rainiall Snoqualmi Falls different from mean rainfall in Seattle. (Clearly and the hypotheses you're testing. and gives full and onclusion) 4. ome year the United States, 4.217 million babies were born Of these, 2,173 million were male and 2.074 million were female. With very few exceptions (e.g. identical twins). sexes of the bables indepen we can binomial distributio model number of pabies that female. Let p be the probability that random (future) newborn female. (a) What percentage of the bables were female? (To get credit for this question you must give your answer percentage and you must round appropriately.) (b) Suppose wish test the null hypothesis that the probability baby is female is 50% Write down null and alternative hypotheses in mathematical this test. (c) Find the P-value. using both Binomial probability and Normal ap- proximation (Carefully show your work and R eodes.) (d) Using the Central Limit Theorem find 95% onfidence interval forthe probability that abirthis female. (e) Explain what thisconfidence interva means without using the word "confi-dent." (f) The P-value your test part isbasicall zero Fromt confidence interval, write sentence your conclusion abou the probability that random new is female 5. The basketball pinyer Steph Curry sometimes shoots free throws with his mouthguard n his mouth shoots throws with his mouthguard outside ( his mouth. His free throw statistics for one season were: Free throws with mouthguard in: 110 completed 13 missed (89 4%) Free throws with mouthguard out 198 completed 16 missed (92.5%) His observed free throw completion rate was slightly higher wher his was outside his mouth However we should check whether the difference could be plausibly explained as luck (a) Using Central Limit Theorem, find an approximate 95% forthe probability that Curry completes free throw Give numerical answer. (b) Using Central Limit Theorem find approximate 95% confidence interva forthe probability that Curry completes throw out. (c) Suppose wish test hypothesis Curry's probability com-pleting free throw sthe same with mouthguard with mouthguard out. The P-value for such test 0.33. What does this P-value tell you? Explain. 6. Rosene (1950) studied how quickly hairs on radish roots absorbed water when they were immersed For each eleven radishes, measured the rate water for young root hair and old root hair that radish. The data given below. Radish Table Radish root hair absorption data. Rates are cubic microns per square micron per minute For each pair. the "Young" number bigger than the FOld" number even without test it's clear that young roots take water more quickly. But how much more quickly? (a) Explain what test should consider based the data and context and why (Hint: 1-sample 2-sample test, z-test off-test (b) Usea normal ploto differences (old minus young) and the mole sizeto explain hesitant do such atest (the one you proposed nthe previous question these minus young). (c) Explain why we should not take the logs these diflerences minus young.) (d) Instead fusing we can look young. This ratio looks come from amuch closer normal distribution Write codeto 90% confidence interval the average value ratio. 7. The basketball player Stephen Curry was the Most Valuable Plaver for the 2015 16 season Hei known being (throwine the basketball into the hoop) long distance. Data Canvas ontains the shots during the 2015 or these shots, sos them were uccessful. data randor independent samples (this isn't quite true The variables distance: from the venue: "Home" was (in Oakland). "Away" if it was somewhere . nade: Load the currydist read txt". currydist read Then von can extract variables frame using the dollar sign. e.g. for the distance that R h case-sensitive.) (a) Create two R: one containing distances for Curry's shots home and one containing the distances for Curry's Remember that we usesquare brackets for subsetting ! - Draw graph that compares the full distributions of these variables and describe your (Note: Boxplots distributions. By "distribution" the PDF CDF. You should make visually nivvions which distribution (b) show that the d'stance Curry's shots different from the distance o: furry shots awny7 Perform appropriate interval Clearly parameter and hypotheses testing. and give (Le. "Reject" "Don't (c) Show that the met or,1 they why they

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