(a) If you toss the coin 10 times, it will come up heads 5 times. (b) If you toss the coin a very large number of times, the proportion of heads will be close to 0.5.
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Here use basic concept of expectation and MOE
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- Problem: An administer claims that the proportion of students who pass a particular test given to all college freshmen is 77.32%. To test the claim an SRS of size 199 test scores was collected. The sample had 74 students pass the test. Find the test statistic.For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.Santa Fe black-on-white is a type of pottery commonly found at archaeological excavations at a certain monument. At one excavation site a sample of 594 potsherds was found, of which 368 were identified as Santa Fe black-on-white. (a) Let p represent the proportion of Santa Fe black-on-white potsherds at the excavation site. Find a point estimate for p. (Round your answer to four decimal places.)(b) Find a 95% confidence interval for p. (Round your answers to three decimal places.) lower limit upper limitMatt thinks that he has a special relationship with the number 2. In particular, Matt thinks that he would roll a 2 with a fair 6-sided die more often than you'd expect by chance alone. Suppose p is the true proportion of the time Matt will roll a 2. (a) State the null and alternative hypotheses for testing Matt's claim. (Type the symbol "p' for the population proportion, whichever symbols you need of " "not" and express any values as a fraction e.g. p = 1/3) Ho = H₂ = (b) Now suppose Matt makes n = 38 rolls, and a 2 comes up 8 times out of the 38 rolls. Determine the P-value of the test: P-value= (c) Answer the question: Does this sample provide evidence at the 5 percent level that Matt rolls a 2 more often than you'd expect? (Type: Yes or No)
- For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.In a combined study of northern pike, cutthroat trout, rainbow trout, and lake trout, it was found that 34 out of 806 fish died when caught and released using barbless hooks on flies or lures. All hooks were removed from the fish. (a) Let p represent the proportion of all pike and trout that die (i.e., p is the mortality rate) when caught and released using barbless hooks. Find a point estimate for p. (Round your answer to four decimal places.)(b) Find a 99% confidence interval for p. (Round your answers to three decimal places.) lower limit upper limitIf a coin is flipped 225 times and the number of Hs is 75. Compute the proportion of Hs. Round to three places.Suppose that the result of a public opinion poll shows that just 10% of people would be willing to give up their cell phones for 1 week in exchange for $100. How many people would need to be surveyed in order to have a margin of error of ±2%?
- Sean thinks that he has a special relationship with the number 6. In particular, Sean thinks that he would roll a 6 with a fair 6-sided die more often than you'd expect by chance alone. Suppose pis the true proportion of the time Sean will roll a 6. (a) State the null and alternative hypotheses for testing Sean's claim. (Type the symbol "p" for the population proportion, whichever symbols you need of "", "-", "not =" and express any values as a fraction e.g. p = 1/3) Ho= Ha (b) Now suppose Sean makes n = 30 rolls, and a 6 comes up 6 times out of the 30 rolls. Determine 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 Sean rolls a 6 more often than you'd expect? (Type: Yes or No) 4Matt thinks that he has a special relationship with the number 2. In particular, Matt thinks that he would roll a 2 with a fair 6-sided die more often than you'd expect by chance alone. Suppose p is the true proportion of the time Matt will roll a 2. (a) State the null and alternative hypotheses for testing Matt's claim. (Type the symbol "p" for the population proportion, whichever symbols you need of "", "=", "not =" and express any values as a fraction e.g. p = 1/3) Ho p= 1/6 = Ha= p > 1/6 (b) Now suppose Matt makes n = 34 rolls, and a 2 comes up 7 times out of the 34 rolls. Determine the P-value of the test: P-value = | (c) Answer the question: Does this sample provide evidence at the 5 percent level that Matt rolls a 2 more often than you'd expect? (Type: Yes or No) noA farmer only grows apple and orange trees in his orchard. 40% of his trees are apple trees. He is concerned that a parasite may be infecting his trees. The probability of the parasite infecting a given apple tree is 5% and the probability of the parasite infecting a given orange tree is 3%. Please give your answers to 3 decimal places, for example 0.305. a) What proportion of his trees are infected by the parasite? Your answer is 1 b) If a given tree is not infected, what is the probability that this tree was an apple tree? Your answer is
- The American Heart Association is about to conduct an anti-smoking campaign and wants to know the fraction of Americans over 38 who smoke. Step 1 of 2: Suppose a sample of 273 Americans over 38 is drawn. Of these people, 79 smoke. Using the data, estimate the proportion of Americans over 38 who smoke. Enter your answer as a fraction or a decimal number rounded to three decimal places. Step 2 of 2: Suppose a sample of 273 Americans over 38 is drawn. Of these people, 79 smoke. Using the data, construct the 85% confidence interval for the population proportion of Americans over 38 who smoke. Round your answers to three decimal places. Lower end point, upper end pointThe number of employees working for Fly Me to the Moon Airlines in 2005 was 16,633, with an expected decrease of 4.4%4.4% per year. At the rate of decrease given, what is the expected number of employees working at Fly Me to the Moon Airlines in 2006? Round your answer to the nearest integer.For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.Santa Fe black-on-white is a type of pottery commonly found at archaeological excavations at a certain monument. At one excavation site a sample of 580 potsherds was found, of which 370 were identified as Santa Fe black-on-white. (a) Let p represent the proportion of Santa Fe black-on-white potsherds at the excavation site. Find a point estimate for p. (Round your answer to four decimal places.)(b) Find a 95% confidence interval for p. (Round your answers to three decimal places.) lower limit upper limit