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statistics econometrics

Questions and Answers of Statistics Econometrics

compute directly the four population summary sta- tistics estimated in part (a), and discuss the quality of these estimates.
Refer to the data of Exercise 21, which provide test scores of a class of forty students. (a) Based on the data groupings used in constructing your histogram, estimate (i) The population mean. (ii)
A sample of fifty personal property insurance policies found the following numbers of claims over the past 2 years. NUMBER OF CLAIMS NUMBER OF POLICIES 0 1 2 4 5 6 21 13 $ 4 2 3 2 (a) Find the mean
The accompanying table shows percentage returns for the twenty-five largest U.S.com- mon stock mutual funds for 1989, through Thursday, November 12, 1989. (a) Construct a histogram to summarize these
The accompanying table shows the percentage decreases in share values for the twenty- five largest U.S. common stock mutual funds on Friday, November 13, 1989. Construct an appropriate histogram to
The accompanying table shows test scores of the forty students in a class. Construct an up- propriate histogram to summarize these data. 54 56 8 59 60 62 62 67 68 70 70 73 73 75 77 79 81 81 83 85 89
Tires of a particular brand have lifetimes with mean 29,000 miles and standard deviation 3,000 miles. (a) Find a range in which it can be guaranteed that 75% of the lifetimes of tires of this brand
In one year, earnings growth of the 500 largest U.S. corporations averaged 9.2%; the stan- dard deviation was 3.5%. (a) Find a range in which it can be guaranteed that 84% of these earnings growth
An auditor finds that the values of a corporation's accounts receivable have mean $295 and standard deviation $63. (a) Find a range in which it can be guaranteed that 60% of these values lie. (b)
Consider the following four populations: (a) 1, 2, 3, 4, 5, 6, 7, 8 (b) 1.1, 1, 1, 8, 8, 8, 8 (c) 1.1. 4, 4, 5, 5, 8, 8 (d) -6, -3, 0, 3, 6, 9, 12, 15 All of these populations have the same mean.
A sample of twelve business statistics students found the following figures for number of hours spent studying the course material in the week before the final exam: 12 7 4 16 21 5 9311 14 10 6 (a)
Refer to the data of Exercise 7 on bonus payments as a percentage of total compensation for a sample of twelve senior executives. (a) Find the sample standard deviation. (b) Find the interquartile
The data of Exercise 6 show percentage sales increases for ten stores. (a) Find the population variance and standard deviation.(b) Find the range. (c) Find the interquartile range.
Refer to the data of Exercise 5 on a sample of ten test scores. (a) Find the sample variance and standard deviation. (b) Find the mean absolute deviation. (c) Find the interquartile range.
The data of Exercise 4 show ratings of dormitory food service given by a sample of eight students. (a) Find the sample variance and standard deviation. (b) Find the interquartile range.
Refer to the data of Exercise 3 on a sample of ten forecasts of the percentage growth in the consumer price index. (a) Find the sample variance and standard deviation. (b) Find the interquartile
(a) Find the population variance and standard deviation. (b) Find the mean absolute deviation. (e) Find the range. (d) Find the interquartile range.
Refer to the percentage assessments data of Exercise
Refer to the data of Exercise 1 on weekly complaints received by a store's customer ser- vice department over a 10-week period. (a) Find the population variance and standard deviation. (b) Find the
Develop a realistic business example in which the most appropriate measure of central tendency is (a) The mean. (b) The median, (c) The mode.
A sample of twelve senior executives found the following results for percentage of total compensation derived from bonus payments: 15.8 7.3 28.4 18.2 15.0 24.7 13.1 10.2 29.3 34.7 16.9 25.3 (a) Find
A department store chain has ten stores in a state. After a review of sales records, it was found that compared with the same period last year, the following percentage increases in dollar sales had
A corporation recruiting business graduates was particularly interested in hiring numerate graduates. To check on the numeracy of applicants, a test of fifty questions was developed. In a pilot
A sample of eight students, living in campus dormitories, were asked to rate on a scale from one (poor) to seven (excellent) the quality of dormitory food service. The ratings were 2 4 2 3 5 4 3 2
The ten business economists in a sample were asked to predict the percentage growth in the consumer price index over the next year. The forecasts were 3.6 3.1 3.9 3.7 3.5 3.7 3.4 3.0 3.6 3.4 (a) Find
A company owns twelve commercially zoned parcels of land. The assessment rates (in) percentages) assigned to these in 1994 were 21 22 27 36 22 29 22 23 22 28 36 33 For this population: (a) Find the
A department store manager is interested in the number of complaints received by the cus- tomer service department about the quality of electrical products sold by the store. Records over a 10-week
Does minimum wage legislation affect the level of unemployment?
Are utilities more profitable in areas where they have local monopoly power than where they are subject to competition?
Are companies whose dividends are a high percentage of total cash flow viewed as high or low risk?
If General Motors increases the price of mid-size cars by 5%, what will be the effect on the sales of these cars?
Does the rate of growth of the money supply influence the inflation rate?
You are going take a sample of 500 gm blocks of cheese. You know they are approximately normal (µ, σ2) where σ2 = 22. You have a precise normal(502, 12) prior for µ because this is what the the
You are going take a sample of measurements of specific gravity of a chemical product being produced. You know the specific gravity measurements are approximately normal (µ, σ2) where σ2 = .0052.
You are going to conduct a survey of the students in your university to find out whether they read the student newspaper regularly. Based on your friends opinions, you think that a strong majority of
You are going to conduct a survey of the voters in the city you live in. They are being asked whether or not the city should build a new convention facility.You believe that most of the voters will
In the previous two problems we found the posterior distribution of the slope of y on x, the rate of weevil infestation for endophyte infected and noninfected ryegrass. Let β1 be the slope for
For ryegrass that was not infected with endophyte the following data were observed:(a) Plot a scatterplot of number of ryegrass plants versus the infestation rate.(b) The relationship between
Endophyte is a fungus Neotyphodium lolli that lives inside ryegrass plants. It does not spread between plants, but plants grown from endophyte-infected seed will be infected. One of its effects is
In Chapter 3, Exercise 7, we were looking at the relationship between log(mass)and log(length) for a sample of 100 New Zealand slugs of the species Limax maximus from a study conducted by Barker and
is known. Use a normal (0, 102)prior for β. What is the posterior distribution of β.(f) Find a 95% credible interval for β.(g) Perform a Bayesian test of H0 : β ≤ 0 versus H1 : β > 0 at the 95
A textile manufacturer is concerned about the strength of cotton yarn. In order to find out whether fiber length is an important factor in determining the strength of yarn, the quality control
The Police Department is interested in determining the effect of alcohol consumption on driving performance. Twelve male drivers of similar weight, age, and driving experience were randomly assigned
A researcher is investigating the relationship between fuel economy and driving speed. He makes six runs on a test track, each at a different speed, and measures the kilometers travelled on one liter
A researcher is investigating the relationship between yield of potatoes (y) and level of fertilizer (x.) She divides a field into eight plots of equal size and applied fertilizer at a different
A researcher measured heart rate (x) and oxygen uptake (y) for one person under varying exercise conditions. He wishes to determine if heart rate which is easier to measure can be used to predict
One of the advantages of Bayesian statistics is that evidence from different sources can be combined. In Exercise 6 and Exercise 14, we found posterior distributions of µd using data sets from two
The experiment described in Exercise 6 was repeated on another set of 7 cows, McLeay, Carruthers, and Neil (1997). However, in this case, the second treatment was given to the same set of 7 cows that
Are young New Zealand women having their children at a later age than previous generations?(a) Out of the 314 women in the age group 25-29, 136 report having given birth to their first child before
Family formation patterns in New Zealand have changed over the time frame covered by the survey. New Zealand society has become more accepting of couples co-habiting (living together before or
Are younger New Zealand women marrying at a later age than previous generations of New Zealand women? To shed light on this question, we look at the proportions of Zealand women who report having
Are younger New Zealand women becoming sexually active at an earlier age than previous generations of New Zealand women? To shed light on this question, we look at the proportions of Zealand women
Are younger New Zealand women more likely to be in paid employment than previous generations of New Zealand women? To shed light on this question, we will look at the current employment status of two
Have the educational qualifications of younger New Zealand women changed from those of previous generations of New Zealand women? To shed light on this question, we will compare the educational
Glass fragments found on a suspect’s shoes or clothes are often used to connect the suspect to a crime scene. The index of refraction is the fragments are compared to the refractive index of the
Cattle being ruminants have multiple chambers in their stomaches. Stimulating specific receptors causes reflex contraction of the reticular groove and swallowed fluid then bypasses the reticulo-rumen
A thermal power station discharges its cooling water into river. An environmental scientist wants to determine if this has adversely affected the dissolved oxygen level. She takes samples of water
Independent random samples of ceramic produced by two different processes were tested for hardness. The results were:(a) We will assume that the observations come from normal(µ1, σ2) and
The quality manager of a dairy company is concerned whether the levels of butterfat in a product are equal at two dairy factories which produce the product.He obtains random samples of size 10 from
A consumer testing organization obtained samples of size 12 from two brands of emergency flares, and measured the burning times. They are:(a) We will assume that the observations come from
The Human Resources Department of a large company wishes to compare two methods of training industrial workers to perform a skilled task. Twenty workers are selected, and 10 of them are randomly
A medical researcher collected the systolic blood pressure reading for a random sample of n = 30 female students under the age of 21 who visited the Student’s Health Service. The blood pressures
The local consumer watchdog group was concerned about the cost of electricity to residential customers over the New Zealand winter months (Southern Hemisphere). They took a random sample of 25
The statistician buys ten used balls that have been recovered from a water hazard. He drops each from a height of one meter and measures the height in centimeters it returns on the first bounce. The
A statistician buys a pack of 10 new golf balls, and drops each golf ball from a height of one meter, and measures the height in centimeters it returns on the first bounce. The ten values are:79.9
We will use the Minitab macro NormGCP.mac to find the posterior distribution of the normal mean µ when we have a random samples of size n of normal(µ, σ2) observations with known σ2 = 22, and we
Repeat part (a) with a normal(30, 42) prior, storing the likelihood and posterior in c5 and c6.
26.3 28.03 28.5 26.3 31.9 28.5 27.2 20.9 27.5 28.0 18.6 22.3 25.0 31.5 Use NormNP.mac to find the posterior distribution g(µ|y1,...,y15, where we choose a normal (m = 20, s2 = 52) prior
We will use the Minitab macro NormNP.mac to find the posterior distribution of the normal mean µ when we have a random sample of size n from a normal (µ, σ2) distribution with known σ2, and we
Instead of thinking of a random sample of size n = 16, let’s think of the sample mean as a single observation from its distribution.(a) What is the distribution of y¯? Calculate the observed value
Instead, combine all the observations together to give a random sample of size n = 16, and use NormDP.mac to find the posterior distribution where we go back the original prior that had all the
Suppose another 6 random observations come later. They are: 6.22 3.99 3.67 6.35 7.89 6.13 Use NormDP.mac to find the posterior distribution, where we will use the posterior after the first ten
Use the Minitab macro NormDP.mac to find the posterior distribution of the mean µ when we have a random sample of observations from a normal (µ, σ2), where σ2 is known, and we have a discrete
The Houhora site in Northland (top of North Island) New Zealand is one of the sites of early human inhabitation that New Zealand archeologists have investigated, in trying to determine when the
New Zealand was the last major land mass to be settled by human beings.The Shag River Mouth in Otago (lower South Island), New Zealand, is one of the sites of early human inhabitation that New
The Houhora site in Northland (top of North Island) New Zealand is one of the sites of early human inhabitation that New Zealand archeologists have investigated, in trying to determine when the
New Zealand was the last major land mass to be settled by human beings.The Shag River Mouth in Otago (lower South Island), New Zealand, is one of the sites of early human inhabitation that New
An engineer takes a sample of 5 steel I beams from a batch, and measures the amount they sag under a standard load. The amounts in mm are: 5.19 4.72 4.81 4.87 4.88 It is known that the sag is normal
The standard process for making a polymer has mean yield 35%. A chemical engineer has developed a modified process. He runs the process on 10 batches and measures the yield (in percent) for each
The city health inspector wishes to determine the mean bacteria count per liter of water at a popular city beach. Assume the number of bacteria per liter of water is normal with mean µ and standard
The city health inspector wishes to determine the mean bacteria count per liter of water at a popular city beach. Assume the number of bacteria per liter of water is normal with mean µ and standard
You are the statistician responsible for quality standards at a cheese factory.You want the probability that a randomly chosen block of cheese labelled"1 kg" is actually less than 1 kilogram (1000
Comparing Bayesian and frequentist estimators for π. In Chapter 1 we learned that the frequentist procedure for evaluating a statistical procedure, namely looking at how it performs in the long run,
In the same study of water quality, n = 87 samples were taken from streams in municipal catchments. Out of these y = 8 had a high Campylobacter level.Let π be the true probability that a sample of
In the same study of water quality, n = 176 samples were taken from streams having a high environmental impact from sheep farming. Out of these y = 24 had a high Campylobacter level. Let π be the
In the same study of water quality, n = 145 samples were taken from streams having a high environmental impact from dairying. Out of these y = 9 had a high Campylobacter level. Let π be the true
In the study of water quality in New Zealand streams documented in McBride et al. (2002) a high level of Campylobacter was defined as a level greater than 100 per 100 ml of stream water. n = 116
The standard method of screening for a disease fails to detect the presence of the disease in 15% of the patients who actually do have the disease. A new method of screening for the presence of the
Let π be the proportion of students at a university who approve the governments policy on students allowances. The students newspaper is going to take a random sample of n = 30 students at a
Repeat the previous question with a uniform prior for π.
We will use the Minitab macro BinoGCP.mac or the equivalent R function to find the posterior distribution of the binomial probability π when the observation distribution of Y |π is binomial (n, π)
Repeat part (a) with a beta (2, 4) prior, storing the likelihood and posterior in c5 and c6.
We will use the Minitab macro BinoBP.mac or the equivalent R function to find the posterior distribution of the binomial probability π when the observation distribution of Y |π is binomial(n, π)
The same study found that y = 6 out of n = 87 samples within municipal catchments contained Giardia cysts.(a) What is the distribution of y, the number of samples containing Giardia cysts?(b) Let π
The same study found that y = 10 out of n = 174 samples identified as having a heavy environmental impact from pastoral (sheep) farms contained Giardia cysts.(a) What is the distribution of y, the
The same study found that y = 12 out of n = 145 samples identified as having a heavy environmental impact from dairy farms contained Giardia cysts.(a) What is the distribution of y, the number of
In a research program on human health risk from recreational contact with water contaminated with pathogenic microbiological material, the National Institute of Water and Atmosphere (NIWA) instituted
You are going to take a random sample of voters in a city in order to estimate the proportion π who support stopping the fluoridation of the municipal water supply. Before you analyze the data, you
Sophie, the editor of the student newspaper, is going to conduct a survey of students to determine the level of support for the current president of the students association. She needs to determine
A city is considering building a new museum. The local paper wishes to determine the level of support for this project, and is going to conduct a poll of city residents. Out of the sample of 120

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