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mathematics
statistics

Questions and Answers of Statistics

Repeat Problem 15.1.5 using the data set in DS 15.1.2 and for the null hypothesis that the median of the distribution is equal to 40 against a two-sided alternative hypothesis. Problem 15.1.5 Suppose
Use the sign test and the signed rank test to analyze the paired data set of assembly times given in DS 9.2.1. Why might it be expected that the signed rank test is a better test procedure than the
Use the sign test and the signed rank lest to analyze the paired data set of adherent red blood cells given in DS 9.2.2. Do you find any evidence of a difference between the two stimulation
Use the sign lest and the signed rank test to analyze the paired data set of calculus scores given in DS 9.2.4. Do you find any evidence of a difference between the two teaching methods? How much
Recall that DS 6.1.4 shows the service times of customers at a fast-food restaurant who were served between 2:00 and 3:00 on a Saturday afternoon, and that DS 9.3.5 shows the service times of
Recall that DS 6.1.7 shows the weights of a sample, of paving slabs from manufacturer A and that DS 9.3.1 shows the weights of a sample of paving slabs from manufacturer B. Use the Kolmogorov-Smirnov
DS 9.3.3 contains observations of heel-strike force for a runner on a treadmill with and without a damped feature activated. Use plots of the empirical cumulative distribution functions and the
Use the rank sum test procedure to analyze the two samples in DS 15.2.1. (a) What is SA? (b) What is UA? (c) Is the value of UA consistent with the observations from population A being larger or
Repeat Problem 15.2.4 using the data set in DS 15.2.2. Problem 15.2.4 Use the rank sum test procedure to analyze the two samples in DS 15.2.1. (a) What is SA? (b) What is UA? (c) Is the value of UA
Use the rank sum test to analyze the data set in Figure 9.20 concerning Example 51 on acrophobia treatments. Let population A be with the standard treatment and population B be with the new
Recall that DS 6.1.8 contains a sample of paint thicknesses from production line A and that DS 9.3.2 contains a sample of paint thicknesses from production line B. (a) Use the Kolmogorov-Smirnov test
Recall that DS 9.3.4 contains the results of an experiment to compare the bleaching effectiveness of two levels of hydrogen peroxide, a low level and a high level. Use the rank sum test to assess
Use the Kruskal-Wallis test procedure to analyze the data in DS 11.1.1. (b) What are the average ranks 1., 2., and 3.? (c) What is the value of the test statistic H? (d) Write down an expression
The data set in DS 11.2.6 concerns an experiment to compare three different assembly methods for an electric motor. Use the Friedman test procedure to investigate whether there is evidence of any
DS 11.2.7 contains the commissions obtained by five agents in a realtor's office. Use the Friedman test procedure to investigate whether there is evidence of any real difference in the performances
The data set in DS 11.2.8 concerns an experiment to compare four different formulations of a detergent. Use the Friedman test procedure to investigate whether there is evidence of any difference
Use the Kruskal-Wallis test procedure to analyze the data in DS 11.1.2.(a) Find the ranks rtj and the average ranks 1., 2., 3, and 4..(b) What is the value of the test statistic H?(c) Write down
The data set in DS 11.1.3 concerns the infrared radiation readings from an energy source measured by a particular meter with three different background radiation levels.(a) Use the Kruskal-Wallis
DS 11.1.4 contains the times taken to perform a task using three different keyboard layouts for the numerical keys. Use the Kruskal-Wallis test procedure to investigate whether the different layouts
DS 11.1.6 contains the assembly times of computers for three different assembly methods. Use the Kruskal-Wallis test procedure to investigate whether there is any evidence that one assembly method is
Use the Friedman test procedure to analyze the data in DS 11.2.1.(a) What are the average ranks 1., 2., and 3.?(b) What is the value of the test statistic S?(c) Write down an expression for the
Use the Friedman test procedure to analyze the data in DS 11.2.2.(a) Find the ranks rij and the average ranks 1., 2., 3., and 4..(b) What is the value of the test statistic 5?(c) Write down an
The data set in DS 11.2.3 concerns the brightness measurements for b = 7 batches of kaolin processed through k = 3 calciners.(a) Use the Friedman test procedure to investigate whether the calciners
DS 11.2.4 contains distances at detection for three radar systems. Use the Friedman test procedure to investigate whether there is evidence of any difference between the radar systems
(a) Is it plausible that the heights are normally distributed with a mean of 70 inches and a standard deviation of 2 inches? (b) Is it plausible that the heights are normally distributed with a mean
Use the Friedman test procedure to analyze the data set in DS 11.4.3 concerning cement strengths.(a) What are the average ranks 1., 2., 3., 4., and 5.?(b) What is the value of the test statistic
DS 11.4.4 contains the results of an experiment to compare five fertilizers. I 'sc the Friedman test procedure to investigate whether there is evidence of any difference between the fertilizers.
The data set in DS II .4.5 concerns the reports of k: = 4 clinics for b = 12 samples of blood.(a) Use the Friedman test procedure to investigate whether the clinics appear to be reporting similar
Recall the data set of soil compressibility measurements given in DS 6.6.6. Construct the empirical cumulative distribution function for this data set. Use the sign test and the signed rank test to
DS 9.6.5 contains the data from an experiment in which a group of 10 subjects had their ocular motor measurements recorded after they had been leading a book for an hour and also after they had been
Oil viscosity values obtained from two engines are given in DS 9.6.6. Use the rank sum test to assess whether there is any evidence that the engines have different effects on the oil viscosity.
Construct the empirical cumulative distribution function for the data set of bamboo shoot heights given in DS 6.6.5. Draw 95% confidence bands around the empirical cumulative distribution function.
Use the sign test and the signed rank test to analyze the paired data set of tire wear given in DS 9.2.3. Do you find any evidence of a difference between the two types of tires? Do you think that
Use the sign test and the signed rank test to analyze the paired data set given in DS 9.6.1 concerning the assimilation of information from video monitors. Do you find any evidence of a difference
Recall that DS 9.6.4 contains data observations of waiting times for a consumer to speak to a company representative on a telephone complaints line both before and after a reorganization. Use the
A researcher compares the bamboo shoot heights in DS 6.6.5 obtained under growing conditions A with the bamboo shoot heights in DS 9.6.3 obtained under growing conditions B. Recall that the growing
Use the rank sum test to analyze the data set in Figure 9.24 concerning Example 53 on kudzu pulping. Let population A be without the addition of anthraquinone and population B be with the addition of
DS 11.4.1 contains Young's modulus measurements for four different types of nanowires. Use the Kruskal-Wallis test procedure to investigate whether there is any evidence of a difference in the types
The data set in DS 11.4.2 concerns the gas mileages of four cars.(a) Use the Kruskal-Wallis test procedure to investigate whether any of the cars are getting better gas mileages than the other
Suppose that when a process is in control a variable can be taken to be normally distributed with a mean of μ0 = 10.0 and a standard deviation of σ = 0.2, and that a control chart is to be
A production process making chemical solutions is in control when the solution strengths have a mean of μ0 = 0.650 and a standard deviation of σ = 0.015. Suppose that it is a reasonable
Suppose that a 2-sigma control chart is used to monitor a variable that can be taken to be normally distributed. (a) What is the probability that an observation will lie outside the control limits
Suppose that a 3-sigma control chart is used. What is the probability that when the process is in control, the first eight points plotted lie on the same side of the center line but within the
DS 16.3.1 contains the sample means i and the sample ranges ri of samples of size n = 4 of a measurement of interest collected at k = 20 distinct time points from a production process. (a) Construct
DS 16.3.2 contains the sample means i and the sample ranges ri of a variable measurement based upon samples of size n = 5, which are collected at k = 25 points in time. (a) Use this data set to
Control charts arc lo be used to monitor the thicknesses of glass sheets. DS 16.3.3 contains the thicknesses in mm of random samples of n = 4 glass sheets collected at k = 24 different times. (a)
Construct a p-chart from the data in DS 16.4.1, which are the number of defective items found in random samples of n = 100 items taken at k = 30 time points. (a) Is there any reason to believe that
Metal rods are spray painted by a machine and a p-chart is to be used to monitor the proportion of rods that are not painted correctly. These defective rods have either an incomplete coverage or a
A paper mill has decided to use a c-chart to monitor the number of imperfections in large paper sheets. The data set in DS 16.4.4 records the number of imperfections found in k = 22 sheets of paper
A random sample of size n = 5 is taken from a batch of size N = 50, and the batch is accepted if the number of defective items found is no larger than c = 2. Use the hypergeometric distribution to
Electrical fuses are sold in boxes of N = 20 fuses, and an acceptance sampling procedure is implemented with a random sample of size n = 3 and a value c = 1. Calculate and compare each value exactly
Ceramic tiles are shipped in very large batches and an acceptance sampling procedure to monitor the number of cracked tiles in a batch has n = 50 and c = 10. Use the binomial approximation to
A company that manufactures soap bars finds that the bars tend to be underweight if too much air is blown into the soap solution so that its density is too low. It is decided to set up a control
A paper mill has decided to implement a control chart to monitor the weight of the paper that it is producing. DS 16.6.1 contains the weights in g/m2 of n = 3 random paper samples collected at k = 22
A factory that packages food products in metal cans has installed an ink jet to spray a date code onto the bottom of the cans. Sometimes the process does not work correctly and the date codes are
In the textile industry c-charts can be used to monitor the number of Maws occurring in segments of fabric. Construct a c-chart from the data set in DS 16.6.3, which records the number of flaws found
An acceptance sampling procedure is being developed to check whether batteries have the required voltage. The batteries are shipped in very large batches, and the voltages of a random sample of n =
A component has an exponential failure time distribution with a mean time to failure of 225 hours. (a) What is the probability that the component is still operating after 250 hours? (b) What is the
A component has an exponential failure time distribution with a mean time to failure of 35 days. (a) What is the probability that the component is still operating after 35 days? (b) What is the
A component has a constant hazard rate of 0.2. (a) What is the probability that the component is still operating at time 4.0? (b) What is the probability that the component fails before time 6.0?
A component has a lognormal failure time distribution with parameters μ = 2.5 and σ = 1.5. (a) What is the probability that the component is still operating at time 40? (b) What is the probability
A component has a lognormal failure time distribution with parameters μ = 3.0 and σ = 0.5. (a) What is the probability that the component is still operating at time 50? (b) What is the probability
A component has a Weibull failure time distribution with parameters a = 3.0 and λ = 0.25. (a) What is the probability that the component is still operating at time 5? (b) What is the probability
A component has a Weibull failure time distribution with parameters a = 4.5 and λ = 0.1. (a) What is the probability that the component is still operating at time 12? (b) What is the probability
A set of n = 30 components arc tested and their average lifetime is = 132.4 hours. (a) If the lifetimes are modeled with an exponential distribution, construct a 99% confidence interval for the
The failure times in hours of n = 20 identical electrical circuits subjected to an intense vibration are given in DS 17.3.1. (a) If the failure times are modeled with an exponential distribution,
Thirty computer chips are tested in a sequential manner. A chip is placed in a circuit and when it fails it is immediately replaced by another chip. The final chip fails 176.5 hours after the
The survival times in hours of a virus under certain conditions are given in DS 17.3.2. (a) If the survival times are modeled with a lognormal distribution, estimate the parameters μ and σ. (b) Use
DS 17.3.3 contains a data set of failure times, where an asterisk represents a right-censored observation. (a) Construct and graph the product limit estimator of the reliability function. (b)
(a) A set of n identical components with reliabilities 0.90 are placed in parallel. What value of n is needed to ensure that the overall system reliability is at least 0.995? (b) In general, how many
The germination time of a seed in days is modeled as having a constant hazard rate of 0.31. (a) What is the probability that a seed has not germinated after 6 days? (b) What is the probability that a
The failure time of a light bulb in days is modeled as a Weibull distribution with parameters a = 2.5 and λ = 0.01. (a) What is the probability that a light bulb is still operating after 120
The times in hours that a conveyor belt operates before a mechanical malfunction occurs are given in DS 17.4.1. (a) If the failure limes are modeled with an exponential distribution, construct a 95%
The times in minutes taken by n = 25 samples of concrete to fracture when subjected to a certain stress are given in DS 17.4.2. (a) If the failure times are modeled with a lognormal distribution,
DS 17.4.3 contains a data set of failure times in days of a certain type of electric motor. Exact failure times are observed when the motor fails to operate correctly and needs replacing.
What is the sample space when a coin is tossed three times? Discuss.
An experiment has three outcomes. I, II and III. If outcome I is twice as likely as outcome II and outcome II is three times as likely as outcome III, what are the probability values of the three
A probability value p is often reported as an odds ratio, which is p / (1 - p). This is the ratio of the probability that the event happens to the probability that the event does not happen. (a) If
An experiment has live outcomes. I, II, III, IV and V. If P(I) = 0.13. P(II) = 0.24, P(III) = 0.07 and P(III) = 0.38, what is P(V)?
Do the GM and Ford returns seem positively correlated? Do you notice any outlying returns? If yes," do outlying GM returns seem to occur with outlying Ford returns?
Compute the log returns for GM and plot the returns versus the log returns? How highly correlated are the two types of returns?
What is the probability that the hedge fund will make a profit of at least $100,000?
What is the probability the hedge fund will suffer a loss?
What is the expected profit from this trading strategy?
What is the expected return? When answering this question, remember that only $50,000 was invested. Also, the units of return are time, e.g., one can express a return as a daily return or a weekly
The daily log returns on a stock are independent and normally distributed with mean 0.001 and standard deviation 0.015. Suppose you buy $1000 worth of this stock. (a) What is the probability that
The yearly log returns on a stock are normally distributed with mean 0.1 and standard deviation 0.2. The stock is selling at $100 today. What is the probability that one year from now it is selling
Suppose the price of a stock at times 1, 2, and 3 are P1 = 95, P2 = 103, and P3 = 98. Find r3(2).
The prices and dividends of a stock are given in the table below.(a) What is R2?(b) What is R4(3)?(c) What is r3?
Let rt be a log return. Suppose that r1, r2, . . . are i.i.d. N(0.06, 0.47). (a) What is the distribution of rt(4) = rt + rt-1 + rt-2 + rt-3? (b) What is P{r1(4) < 2}? (c) What is the covariance
Suppose that X1,X2, . . . is a lognormal geometric random walk with parameters (μ, σ2). More specifically, suppose that Xk = X0exp(r1 + ∙ ∙ ∙ +rk), where X0 is a fixed constant and r1, r2, .
The daily log returns on a stock are normally distributed with mean 0.0002 and standard deviation 0.03. The stock price is now $97. What is the probability that it will exceed $100 after 20 trading
(a) Describe the signs of nonstationarity seen in the time series and ACF plots. (b) Use the augmented Dickey{Fuller tests to decide which of the series are nonstationary. Do the tests corroborate
1. Do the differenced series appear stationary according to the augmented Dickey{Fuller tests? 2. Do you see evidence of autocorrelations in the differenced series? If so, describe these correlations.
Do you see any seasonal differences in the boxplots? If so, describe them.
1.What order of differencing is chosen? Does this result agree with your previous conclusions? 2. What model was chosen by AIC? 3. Which goodness-of-fit criterion is being used here? 4. Change the
Do you think that there is residual autocorrelation? If so, describe this autocorrelation and suggest a more appropriate model for the T-bill series.
Do you see evidence of GARCH effects?
(a) Why do the prediction intervals (blue curves) widen as one moves farther into the future? (b) What causes the the predictions (red) and the prediction intervals to wiggle initially? Include the
This problem and the next use CRSP daily returns. First, get the data and plot the ACF in two ways: library(Ecdat) data(CRSPday) crsp=CRSPday[,7] acf(crsp) acf(as.numeric(crsp)) (a) Explain what

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