Statistics Help on Practice Final

ryyrawnl
timer Asked: Dec 17th, 2014

Question Description

Practice Final  

Hi, I need help with number 3 and 4. Do you think you could help me out? 

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Math 161A: Applied Probability and Statistics I Fall 2013 Exam 3A (December 12) First Name: Last Name: Score: /32 Instructions: 1◦ Write your name CLEARLY in the spaces provided above. 2◦ This paper contains four questions and comprises seven printed pages. 3◦ Answer ALL the questions in the spaces provided. Do not attach additional sheet(s) of paper. 4◦ For each question, do not provide alternative solution(s)—if you do so, only the first solution will be graded. 5◦ You may use a calculator. However, you should lay out systematically the various steps in the calculations; otherwise, no credit will be given. 1. A random sample of size 25 was selected from a population with expected value 120 and variance 1. (a) Find the expected value and the standard deviation of the sampling distribution of the sample mean. [4 pts] (b) Can we determine the exact sampling distribution of the sample mean? Explain. [2 pts] 2 2. A certain type of automobile battery is known to last an average of 1110 days with a standard deviation of 80 days. Suppose that 400 of these batteries are selected. (a) Find the probability that the average length of life of the 400 selected batteries is between 1105 and 1110. [4 pts] (b) Is the probability calculated in (a) exact or approximate? Explain. 3 [2 pts] 3. A sample survey is designed to estimate the proportion of sports utility vehicles being driven in the state of California. A random sample of 500 registrations are selected from a Department of Motor Vehicles database, and 68 are classified as sports utility vehicles. (a) Use a 95% confidence interval to estimate the proportion of sports utility vehicles in California. [4 pts] 4 (b) State the assumptions that are necesssary to ensure that the confidence interval in 3 (a) is valid, and determine if these assumptions are satisfied. [4 pts] (c) Can we conclude that the probability that the proportion of sports utility vehicles in California lies in the interval constructed in 3 (a) is 0.95? Explain. [2 pts] 5 4. In an investigation of the toxin produced by a certain poisonous snake, a researcher prepared 26 different vials, each containing 1 g of the toxin, and then determined the amount of antitoxin needed to neutralize the toxin. The sample average amount of antitoxin necessary was found to be 1.89 mg and the sample standard deviation was 0.42 mg. Previous research had indicated that the true average neutralizing amount was 1.75 mg of antitoxin for every 1 g of toxin. (a) Does the new data contradict the value suggested by prior research? Test the appropriate hypotheses at level of significance 0.05, based on an appropriate rejection region. [6 pts] 6 (b) Calculate the p-value for the value of the test statistic computed in 4 (a). What conclusion would be reached for a significance level of 0.01? Answer the same question for a significance level of 0.10. [4 pts] 7
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