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Let T0(X) be an unbiased estimator of in an estimation problem. Show that any unbiased estimator of ϑ is of the form T(X) = T0(X)- U(X), where U(X) is an "unbiased estimator" of 0.
Statistics and Probability, Statistics
Researchers randomly assigned 25 beginning students of Russian to begin speaking practice immediately and another 25 to delay speaking for 4 weeks. At the end of the semester both groups took a standard test of comprehen ...
Ann and Bill play rock-paper-scissors. Each has a strategy of choosing uniformly at random out of rock, paper, and scissors every round (making independent selections each round). Each round can end in a win, loss, or a ...
In a survey of 2936 adults, 1431 say they have started paying bills online in the last year. Construct a 99% confidence interval for the population proportion. A 99% confidence interval for the population proportion is ( ...
A researcher working at a particular company wants to know if workers' health would improve if they were given extra days 'off. In this company, all workers undergo a standard physical exam twice a year and after each ex ...
The company's cleaning service states that they spend more than 46 minutes each time the cleaning service is there. The company times the length of 37 randomly selected cleaning visits and finds the average is 47.6 minut ...
A restaurant serves hot chocolate that has a mean temperature of 175 degrees with a standard deviation of 8.1 degrees. Find the probability that a randomly selected cup of hot chocolate would have a temperature of less t ...
A company making refrigerators strives for the internal temperature to have a mean of 37.5 degrees with a standard deviation of 0.6 degrees, based on samples of 100. A sample of 100 refrigerators have an average temperat ...
A study if the impact of stress on the amount of beta-endorphins released in the blood was reported. Researchers took beta-endorphin levels for 19 patients 12 hours before surgery and again 10 minutes before surgery. If ...
The service manager for a car dealership reviewed sales records of the past 25 sales of new cars to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate ...
A survey of a random sample of 1000 smartphone owners found that the mean daily time spent communicating on a smartphone was 131.4 minutes. From previous studies, it is assumed that the population standard deviation is 2 ...
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