4. TA Hayden and TA Jiayi were deciding who has to mark the STAT200 assignment first,...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
4. TA Hayden and TA Jiayi were deciding who has to mark the STAT200 assignment first, and chose to flip a coin to decide. They suspect the coin they are using is biased. They decide to test the coin to make inference about the true proportion of heads. (a) If they want the estimate of the population proportion to be correct within 0.05 with 95% confidence, how many times should they flip the coin, assuming p 0.5? [2 marks] (b) Suppose Hayden and Jiayi decide to flip the coin 121 times and observed 87 heads among the 121 results. What is the resulting 95% confidence interval for the true proportion of heads? As always, make sure to state all necessary assumptions and conditions for the confidence interval to get full marks. [3 marks] (c) After taking the sample and calculating the confidence interval above, Jiayi makes the following claim: "There is a 95% chance that the true proportion is within this confidence interval." Explain what is wrong with this claim and what the 95% confidence interval actually means in this context. [2 marks] (d) Hayden is not satisfied with a 95% confidence interval, and wants a higher confidence level. What will happen to the confidence interval if they use a higher confidence level than 95%? [1 mark] (e) Hayden wants to be 100% confident about the true proportion of heads. He proposes making a 100% confidence interval for this proportion. What would a 100% confidence interval for the true proportion heads be? Why is making a 100% confidence interval a bad idea? [2 marks] 4. TA Hayden and TA Jiayi were deciding who has to mark the STAT200 assignment first, and chose to flip a coin to decide. They suspect the coin they are using is biased. They decide to test the coin to make inference about the true proportion of heads. (a) If they want the estimate of the population proportion to be correct within 0.05 with 95% confidence, how many times should they flip the coin, assuming p 0.5? [2 marks] (b) Suppose Hayden and Jiayi decide to flip the coin 121 times and observed 87 heads among the 121 results. What is the resulting 95% confidence interval for the true proportion of heads? As always, make sure to state all necessary assumptions and conditions for the confidence interval to get full marks. [3 marks] (c) After taking the sample and calculating the confidence interval above, Jiayi makes the following claim: "There is a 95% chance that the true proportion is within this confidence interval." Explain what is wrong with this claim and what the 95% confidence interval actually means in this context. [2 marks] (d) Hayden is not satisfied with a 95% confidence interval, and wants a higher confidence level. What will happen to the confidence interval if they use a higher confidence level than 95%? [1 mark] (e) Hayden wants to be 100% confident about the true proportion of heads. He proposes making a 100% confidence interval for this proportion. What would a 100% confidence interval for the true proportion heads be? Why is making a 100% confidence interval a bad idea? [2 marks]
Expert Answer:
Related Book For
Probability and Statistics for Engineers and Scientists
ISBN: 978-0495107576
3rd edition
Authors: Anthony Hayter
Posted Date:
Students also viewed these mathematics questions
-
How many times should a coin be tossed to obtain a probability equal to or greater than .9 of observing at least one head?
-
Suppose that a biased coin that lands on heads with probability p is flipped 10 times. Given that a total of 6 heads results, find the conditional probability that the first 3 outcomes are (a) h, t,...
-
A biased coin has a probability p of resulting in a head. If the coin is tossed twice, what value of p minimizes the probability that the same result is obtained on both throws?
-
A non reactive/conservative contaminant is dumped on the ground level and it leaches to the groundwater vertically and takes half day for reaching the groundwater by travelling through unsaturated...
-
(a) Moberg Company sells three different categories of tools (small, medium, and large). The cost and market value of its inventory of tools are as follows. Determine the value of the company's...
-
1. Solve the problem geometrically. 2. By looking at your graph from part 1, can you determine the shadow price of cheddar? Jason's House of Cheese offers two cheese assortments for holiday gift...
-
Zachary and Carrie Sexton (the Buyers) were searching for a home in the Kings wood neighborhood of Atlanta, Georgia. The Buyers real estate agent learned that Russell and Linda Sewell (the Sellers)...
-
Bell Mountain Vineyards is considering updating its current manual accounting system with a high-end electronic system. While the new accounting system would save the company money, the cost of the...
-
1. Solve the double inequality below. Then graph the solution set on the real number line. -81+3(x-2) < 13
-
Prevosti Farms and Sugarhouse pays its employees according to their job classification. The following employees make up Sugarhouse's staff: Employee Number Name and Address Payroll information...
-
Show that the functions u(x, t) = e-kt (2 sin x+3 cos x) and u(x, t) = ex/(4kt)/t satisfies the one-dimensional heat equation where k is a positive constant. du Pu t x -
-
A big supplier of used cars is rental car companies, who sell their rental cars after they're too used to rent out but are still good. Rental cars are not a substitute or complement for used cars on...
-
Review the implied terms in the Sale of Goods Acts and select the two most important implied terms in the sale of goods. Justify your selection according to the commercial or legal protections...
-
Mo takes out insurance for his new house. The outside of his house has been painted. It looks like painted Brick. Mo thought the house was Brick. Based on this belief, he takes out house insurances...
-
Sophia Mendelsohn, the JetBlue Head of Sustainability, sits down with former U.S. Treasury Secretary Lawrence Summers, TIAA CEO Roger Ferguson, and David Westin on "Bloomberg Wall Street Week." The...
-
If you think about the components of value-percept theory and job characteristics theory, where does "the product" fit in? How can the high satisfaction of Activision Blizzard employees be explained...
-
Suppose the cost of capital is 14% (show your calculations) i) Calculate the payback period for the project. (1 mark) ii) Calculate the NPV of the project. (1 mark) iii) Calculate the IRR for the...
-
Dawson Companys balance sheet information at the end of 2019 and 2020 is as follows: Additional information: The company did not issue any common stock during 2020. Required : Next Level Fill in the...
-
Use the sign lest and the signed rank test to analyze the paired data set of calculus scores given in DS 9.2.4. Do you find any evidence of a difference between the two teaching methods? How much...
-
Twenty players compete in a tournament. In how many ways can rankings be assigned to the top five competitors? In how many ways can the best five competitors be chosen (without being in any order)?
-
Consider again Problem 5.6.3 where the lengths of adult salmon have N(70, 5.42) distributions. (a) If you go fishing with a friend, what is the probability that the first adult salmon you catch is...
-
Let \(X, Y, X_{n}, Y_{n}: \Omega ightarrow \mathbb{R}, n \geqslant 1\), be random variables. a) If, for all n > 1, Xn Yn and if (Xn, Yn) (X, Y), then XIL Y. b) Let X Y such that X, Y ~ B1/2 = (80...
-
Let \(X_{n}, Y_{n}: \Omega ightarrow \mathbb{R}, n \geqslant 1\), be two sequences of random variables. a) If \(X_{n} \xrightarrow{d} X\) and \(Y_{n} \xrightarrow{\mathbb{P}} c\), then \(X_{n} Y_{n}...
-
Let \(X_{n}, Y_{n}: \Omega ightarrow \mathbb{R}^{d}, n \geqslant 1\), be two sequences of random variables such that \(X_{n} \xrightarrow{d} X\) and \(X_{n}-Y_{n} \xrightarrow{\mathbb{P}} 0\). Then...
Study smarter with the SolutionInn App