i12-48. A lady declares that by taking a cup of tea, she can discriminate whether the milk ortea infusion was first added to the cup. It is proposed to test this assertion by means of an experiment with12 cups of tea, 6 made in one way and 6 in the other, and presenting them to the lady for judgement in arandom order.(i) Calculate the probability that on the null hypothesis that the lady has no discrimination power, shewould judge correctly all the 12 cups, it being known to her that 6 are of each kind.(ii) Suppose that the 12 cups were presented to the lady in six pairs, each pair to consist cups of eachkind in a random order. How would the probability of correctly judging with every cup on the same nullhypothesis be altered in this case ?Which of the two designs would you prefer and why ?

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Answered: i12-48. A lady declares that by taking…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Dominique, Clarice, and marco work for a publishing company. The company wants to send two employees to a statistics conference. To be fair, the company decides that the two individuals who get to attend will have their names randomly drawn from a hat. (a) Determine the sample space of the experiment. That is, list all possible simple random samples of size n=2. (b) What is the probability that Clarice and Marco attend the conference? (c) What is the probability that Dominique attends the conference? (d) What is the probability that Marco stays home?
2
An urn contains red balls and blue balls. Let p represent the proportion of red balls. We would like to test Ho: p = 0.5 We choose 10 balls at random with replacement and we reject the null hypothesis if there are less than 2 or more than 8 red balls in the sample. What is the probability of a Type II error if in fact p=0.3? pbinom(7,10,0.3)-pbinom (2,10,0.3) pbinom(8,10,0.3)-pbinom (1,10,0.3) pbinom(8,10,0.3)-pbinom (2,10,0.3) pbinom(7,10,0.3)-pbinom (1,10,0.3)
A store owner wanted to determine if more than 5% of customers made a purchase after he sent out a text. He sent out 300 texts to 300 randomly selected customers. Out of those 300, 17 made purchases. Is this evidence that if he sent out texts to all of his customers more than 5% would make purchases? What is the appropriate null and alternative hypothesis? Ho: p= 0.05 Ha: p> 0.05 O Ho: phat = 0.05 Ha: phat > 0.05 O Ho: p= 0.056 Ha: p > 0.056 O Ho: mu = 0.05 Hla: mu > 0.05
List all the possible outcomes and determine the values of the random variable in each of the following situations. Use a table for your answers. c.) Three consuls were selected at random one after the other in a meeting of consuls which was attended by 4 Australians and 2 Americans. Let G be number of Australians.
Consider the experiment of rolling five (5) dice, each with 19 sides numbered 1 through 19, where each die is fair, i.e. the sample space consists of equally likely outcomes. Compute the expected sum of the four dice with the highest values. For example, after rolling, the dice show 2, 10, 4, 2, and 13. Since 2 is the lowest value showing on these dice, the sum in this case is 2 + 10 + 4 + 13 = 29. We gave two approaches to a similar problem in class: • An inefficient algorithm for computing the expected value. • An efficient computation using linearity of expected value. Either method is fine, but consider the larger potential for rounding error using the algorithm. Such error is completely avoidable using either method, however, so your answer is expected to be accurate to four decimal places.
In a recent Super Bowl, a TV network predicted that 25 % of the audience would express an interest in seeing one of its forthcoming television shows. The network ran commercials for these shows during the Super Bowl. The day after the Super Bowl, and Advertising Group sampled 138 people who saw the commercials and found that 42 of them said they would watch one of the television shows. Suppose you are have the following null and alternative hypotheses for a test you are running: Ho:p Ha:p + 0.25 = 0,25 Calculate the test statistic, rounded to 3 decimal places
2. A certain health magazine stated * that 14% of men said they used exercise to reduce stress. At a=0.05 test the claim wherein, from a random sample of 100 men who were selected, 10 said that they used exercise to relieve stress. Which of the following is the appropriate null hypothesis of the problem? A. p = 14% B. p ≤ 14% C. p≥ 14% D. p 14% O A. B. D.
Q1 Suppose a drug company designs to develop a new drug to prevent colds. The company states that the drug is equally effective for men and women. To test this claim, they choose a simple random sample of 100 women and 200 men from a population of 100,000 volunteers. At the end of the study, 38 women caught a cold; and 102 men caught a cold. (a) Based on these findings, can we reject the company's claim that the drug is equally effective for men and women? Use a 0.05 level of significance. (b) Find the 95% confidence interval for the difference between the proportions of women and men caught a cold. (c) Are the results of (a) and (b) consistent? Explain briefly.

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