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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.
suppose the joint pdf of lifetimes of a certain part and a spare is given byfx y e?xy 0 lt x lt ? 0 lt y lt ?and zero
Compute F and perform the appropriate F test. Use α = .05. (to 2 decimals). Perform a t test for the significance of β1. Use α = .05. t test statistic = (to 2 decimals)
What is the sample size for this poll? That's a much larger sample than standard sample surveys. In spite of this, we can't trust the result to give good information about any clearly defined population. Why?
At the .05 level of significance, is there convincing evidence that the number of absences per employee has increased?
For the following scores, find the (a) mean, (b) median, (c) sum of squared deviations, (d) variance, and (e) standard deviation:
Make a probability distribution chart using reduced fractions to show the following information: The chart below shows the number of committee members who attended a meeting.
a study on crime indicated that 3.1 car thefts occur each minute in the usa. assume that the distribution of thefts per
She decides to sample lakes by randomly dropping grains of rice on the map and measuring the area of the lakes hit by the rice. Comment on whether or not you think this is a good sampling plan.
Policy Pollsters is a market research firm specializingin political polls. Records indicate in past elections,when a candidate was elected, Policy Pollsters hadaccurately predicted this 80 percent of the time andthey were wrong 20% of the time.
You want to determine if the sample result gives good evidence that the true amount of the compound is not equal to 2 gms. Carry out the test, find the P-value, and state your conclusion.
question a black and red die are thrown and let x be a random variable denoting the sum of the dice.a. find all sample
What are the critical values for z on a one-tailed test if alpha = .01? .001? What would the critical values be at both levels of significance if it was a two-tailed test?
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