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Question: Once upon a time, a famous statistician ordered tea to a lady. The lady claimed that she could tell whether milk had been added to the cup before or after the tea. The statistician decided to run some experiments to test her claim.
(a) The lady is given 6 cups of tea, where it is known in advance that 3 will be milk- first and 3 will be tea-first, in a completely random order. The lady gets to taste each and then guess which 3 were milk-first. Assume for this part that she has no ability whatsoever to distinguish milk-first from tea-first cups of tea. Find the probability that at least 2 of her 3 guesses are correct.
(b) Now the lady is given one cup of tea, with probability 1/2 of it being milk-first. She needs to say whether she thinks it was milk-first. Let p1 be the lady's probability of being correct given that it was milk-first, and p2 be her probability of being correct given that it was tea-first. She claims that the cup was milk-first. Find the posterior odds that the cup is milk-first, given this information.
Assume that we will randomly select a sample of 64 measurements from a population having a mean equal to 20 and a standard deviation equal to 4.
Given that the sample mean is x¯=93.81, and the sample standard deviation is s=4.65, determine if there are any outliers. (We will define an outlier to be any data value outside of the x¯+_2s range.)
The baseball World Series consists of up to seven games. The first team to win four games wins the series. The first two are played at one team's home ballpark.
At the 0.05 level of significance, can we conclude that Tom's filtering system is effective in reducing the weekly number of spam messages an employee receives?
Of the subpopulation of customers who order in the evening, consider the proportion who are female. Similarly, of the subpopulation of customers.
Intuitively, how many times would you expect the ball to wind up in a green slot?- Use the formula for expected value to verify your intuition.
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how can you answer the dual simplex question with maximization objective functionif you have to solve the m-method on
Find μW, σW, and the standardized rank sum statistic. Then give an approximate P-value using the Normal approximation with the continuity correction. What do you conclude?
Lenght Of Pregnancy. A woman wrote to Dear Abby and claimed that she gave birth 309 days after a visit from her hushand , who was in the Navy. Lengths of pegnancies have a mean of 268 days and a standard deviation of 15 days. Find the z score for 308..
What is the probability that there will be a loss rather than a profit?- What is the probability that the profit will be between $10,000 and $20,000?
In talking about cultural and environmental blocks, we discussed the matter of a woman bringing an infant into the workplace and the possible reactions of others. Consider the situation in which a classmate wants to bring her child to school in or..
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