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Here is a simple probability model for multiple-choice tests. Suppose that a student has probability p of correctly answering a question chosen at random from a universe of possible questions. (A good student has a higher p than a poor student.) The correctness of an answer to any specific question doesn't depend on other questions. A test contains n questions. Then the proportion of correct answers that a student gives is a sample proportion from an SRS of size n drawn from a population with population proportion p.
(a) Julie is a good student for whom p = 0.8. Find the probability that Julie scores 77% or lower on a 115 question test.
(b) If the test contains 245 questions, what is the probability that Julie will score 77% or lower? (Use the normal approximation to the sampling distribution to solve this problem.)
(c) How many questions must the test contain in order to reduce the standard deviation of Julie's proportion of correct answers to one-fourth its value for an 100-item test? (Use the sampling approximation to the binomial distribution to solve this problem.)
What are the relevant hypotheses? Perform an appropriate parametric statistical procedure to test these hypotheses and briefly explain your results (a level = 0.05).
In classical hypothesis testing, test statistic is to critical value what the?
Either the seed germinates, or it does not. What is the sample space in this problem? Do the probabilities assigned to the sample space add up to 1? Explain. Are the outcomes in the sample space equally likely?
An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is know to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000.
If population standard deviation is σ = 8 is effect large adequate to be statistically significant? Use two - tailed effect with α = .05
A manufacturer produces and sells chilled, ready-to-eat pasta salad in round lots of 50 serving units each. These items have a very limited shelf life; therefore, if items are made but not sold, they have no value.
Alcohol appears to be involved in a variety of birth defects, including low birth weight and retarded growth. A researcher would like to investigate the effect of prenatal alcohol on birth weight.
Girl B throws 15 times, with a prob. of success = 0.2. And girl C throws 20 times, with a probability of success equal to 0.1. Determine the probability that the target will get hit at least 12 times.
Stock form a normal distribution with a mean of $8.52 with a standard deviation of 2.38. What percentage of the scores lie below $7.42?
Construct a 95% confidence interval estimate for the population proportion of airline travelers who think that the airline fee that is most unreasonable is additional charges to redeem point/miles.
How do you verify that the assumption of a normal distribution is correct if you've only the mean and standard deviation?
An office manager wishes to estimate the mean time required to handle customer complaints. A sample of 38 complaints shows a mean time of 28.7 minutes with a standard deviation of 12 minutes.
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