Homework1

# Homework1 - 4 A fair coin is tossed two times and the...

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STA 3024: Homework 1 (Due Tuesday July 6) 1. Suppose we want to investigate whether or not insomnia can be accurately predicted by education status (no school, middle school, high school, undergraduate, graduate). (a) What is the explanatory variable? Is it categorical or quantitative? (b) What is the response variable? Is is categorical or quantitative? 2. Ten students of a Statistics class are randomly selected. These ten students got an average score of 70 in the class. From this, the instructor estimates that the average score obtained by any student in that class is 70. Identify the population, sample, parameter, and statistic that are relevant to this situation. 3. 20 patients are randomly chosen in a medical study to be given drug A to cure a disease and another 20 patients are chosen to be given drug B. We want to assess which drug is more effective in curing the disease. Is this an observational or experimental study?
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Unformatted text preview: 4. A fair coin is tossed two times, and the events A and B are deﬁned as follows: A: { At least one head is observed } B: { The number of heads observed is odd } (a) Write the sample space. (b) Are A and B independent? (c) Calculate P ( B | A ) . 5. A soccer team has probability of 0.4 of wining any particular game. In a season, it plays 7 conference games. (a) Using binomial distribution, identify n and p . (b) Find the probability that the team wins 4 of its conference games. 6. The mean lifetime of a sample of 100 ﬂorescent light bulbs produced by a company is computed to be 1570 hours with a standard deviation of 120 hours. If μ is the mean lifetime of all bulbs produced by the company, test the hypothesis μ = 1600 hours against the alternative hypothesis μ < 1600 hours , using a level of signiﬁcance 0 . 05 . Find the P value of the test....
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