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a) An article "Does it pay to plead guilty? Differential Sentencing and the Functioning of Criminal Courts" [Law and Society Review, 1981] considered the punishments metered out to 255 individuals found guilty of robbery. All individuals had previous convictions. Of the 191 who pleaded "guilty", 101 were given custodial sentences, whilst of the 64 who pleaded "not guilty" 56 were sent to prison. Present this information in the form of a 2 by 2 contingency table. Carry out a test to determine if the proportion of individuals sent to prison differs significantly for those pleading "guilty" and those pleading "not-guilty"?
b) A promotions panel in a metropolitan police force considered applications from 15 officers who applied for senior positions during one year. The table below records the outcome, classified by gender of the applicant:
Gender
Promoted
Not promoted
Total
Male
7
1
8
Female
2
5
9
6
15
Assuming that these fifteen applications can be considered a random sample of all applications made within the police force calculate the exact probability of this arrangement occurring by chance assuming that males and females are equally likely to be promoted. Test the hypothesis that males are significantly more likely to be promoted.
Which of the following preference orderings, if any, could characterize his preferences? Tell me any/all that apply, and explain how you know this.
Construct a 90% confidence interval on the difference in fraction nonconforming between the two processes."
The cholesterol concentration in the yolks of each of a sample of 22 randomly selected eggs laid by free range chickens were found to have a mean value of 9.38 mg/g of yolk and a standard deviation of 1.62 mg/g.
11% of all books sold are romance genre. If the bookstore sells 316 books on a given day, what is the probability that fewer than 40 are romances, at least 25 are romances, between 25 and 40 are romances?
If the standard deviation is 4.09, how large a sample is needed to get the desired information to be accurate within 0.53 decibels? Show all work.
Based on this sample information find out what percent of variation in starting salaries is described by GPA, and find out the equation that would forecast salary from GPA. Give a scatter plot.
Suppose that it is a presidential election year and Ohio is one of the 'swing' states. Your polling company wants to conduct a presidential preference poll of the citizens of Ohio to predict which candidate will win the election.
Suppose we have a population of scores with a mean (μ) of 975 and a standard deviation (σ) of 15. Assume that the distribution is normal. What percentage of the population will lie between 960 and 990?
What is the sensitivity and specificity of the test? Suppose that 1 out of 500 infants are born with Down's syndrome.
In a random sample 1040 consumers, you find 35% have stopped buying the product. At alpha=0.04, do you have enough evidence to support the claim?
A recent survey of frozen convenience meals found a correlation of r=0.768 between calories and fat content in the sampled meals.
Psychologists once measured 77 variables on a sample of schizophrenic people and a sample of people who were not schizophrenic. They compared the two samples using 77 separate significance tests.
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