Consider Question 3 of this test. Suppose we are interested in testing Ho px = py versus H1: px # PY. %3D (a) Show that the MLE of p, when px = Py = p is the common parameter, is (Px + 2py) /3.
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.If X1 and X2 constitute a random sample of size n = 2from an exponential population, find the efficiency of 2Y1relative to X, where Y1 is the first order statistic and 2Y1and X are both unbiased estimators of the parameterThe time X of a radioactive isotope decays with an expected value of 10 years, and is modeled as an exponential random variable. a) What is the parameter λ of the exponential RV X? b) Compute P(X < 10).
- If the probability mass function of the variable X described in the table is. find variance Y=x^2+4x If you know that the torque is of the second order of the variable X about the origin is equal to 2.85QUESTION 12 Historically, the proportion of people who trade in their old car to a car dealer when purchasing a new car is 48%. Over the previous 6 months, in a sample of 115 new-car buyers, 46 have traded in their old car. To determine (at the 10% level of significance) whether the proportion of new-car buyers that trade in their old car has statistically significantly decreased, what can you conclude concerning the null hypothesis? Reject the null hypothesis Fail to reject the null hypothesisSuppose X1,...,Xn are measurements of the mass of an object. The measurements are normally distributed, with mean equal to mu , the mass of the object, and standard deviation equal to 1 microgram. Find (a) The likelihood function. (b) The log-likelihood function (c) the maximum likelihood estimator for the unknown parameter, and
- Question 16: According to a University Center for Logistics Management, 4% of all merchandise sold in the United States gets returned. A Seattle department store sampled 89 items sold in January and found that 5 of the items were returned.If you have the following null and alternative hypotheses for a test you are running:H0:p=0.04H0:p=0.04Ha:p≠0.04Ha:p≠0.04Calculate the test statistic, rounded to 3 decimal places z=Question 11 A quality-assurance inspector periodically examines the output of a machine to determine whether it is properly adjusted. When set properly, the machine produces nails having a mean length of 2.000 inches, with a standard deviation of 0.070 inches. For a sample of 35 nails, the mean length is 2.025 inches. If the null and alternative hypotheses can be formulated to conclude that the machine is adjusted properly. At 5%% level of significance, find the critical value (s). (-1.43 , 1.43) (-1.435 , 1.435) -1.43 1.435Consider the following 10 measurements about the cohesion of a soil: 12 kPa, 14 kPa, 15 kPa, 14.5 kPa, 16.0 kPa, 18 kPa, 15 kPa, 16.2 kPa, 17. 6 kPa, 13 kPa. Work out the solutions of the following two problems, assuming the cohesion follows the normal and lognormal distributions, respectively. (1) Draw the PDF of the cohesion; (2) Evaluate the probability that the cohesion based on the PDF is less than 5 kPa, 10 kPa, and 15 kPa; (3) Assess the effect of the type of distribution on the results.
- Suppose the table below displays the estimation results from the Logit model Regressor Coefficient (standard error) (log)Income(X1) 0.48 (0.12) Age(X2) 0.03 (0.01) -0.008 (0.02) constant 8.07 (1.16) where the heteroskedasticity-robust standard errors are reported along with the coefficient estimates. How do you interpret the coefficient on log income? Is it significantly different from zero? What is the log odds-ratio for an individual with log income equal to 10 and age equal to 40? Explain what it means.Question 17: A well-known brokerage firm executive claimed that 90% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 100 people, 81% of them said they are confident of meeting their goals.Test the claim that the proportion of people who are confident is smaller than 90% at the 0.05 significance level.The null and alternative hypothesis would be: H0:p≤0.9H0:p≤0.9H1:p>0.9H1:p>0.9 H0:μ≤0.9H0:μ≤0.9H1:μ>0.9H1:μ>0.9 H0:μ≥0.9H0:μ≥0.9H1:μ<0.9H1:μ<0.9 H0:μ=0.9H0:μ=0.9H1:μ≠0.9H1:μ≠0.9 H0:p=0.9H0:p=0.9H1:p≠0.9H1:p≠0.9 H0:p≥0.9H0:p≥0.9H1:p<0.9H1:p<0.9 The test is: two-tailed right-tailed left-tailed The test statistic is: (to 3 decimals)The p-value is: (to 4 decimals)Based on this we: Fail to reject the null hypothesis Reject the null hypothesis.A sample of 9 measurements, randomly selected from a normally distributed population, resulted in x= 2.6, and s= 0.9 Conduct a hypothesis test to verify the claim that the population mean is greater than 2.5 . Use a=.05
