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| m102830 | Two balanced dice are rolled. Refer to Fig. 4.1 on page 159 and determine the probability that the sum of the dice is
In Figure 4.1
a. 6.
b. Even.
c. 7 or 11.
d. 2, 3, or 12. |
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| m102831 | Two balanced dice are thrown, one red and one black. What is the probability that the red die comes up 1, given that the
a. Black die comes up 3?
b. Sum of the dice is 4?
c. Sum of the dice is 9? |
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| m102832 | Two cards are drawn at random from an ordinary deck of 52 cards. Determine the probability that both cards are aces if
a. The first card is replaced before the second card is drawn.
b. The first card is not replaced before the second card is drawn. |
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| m102833 | Two expert French chefs judged chocolate mousse made by students in a Paris cooking school. Each chef ranked the best chocolate mousse as 1.
Use a 0.10 level of signifi cance to test the claim that there is a monotone relation (either way) between ranks given by Chef Pierre and by Chef André.
(a) State the test used.
(b) Give a. State the null and alternate hypotheses.
(c) Find the sample test statistic.
(d) For the sign test, rank-sum test, and Spearman correlation coef ficient test, fi nd the P-value of the sample test statistic. For the runs test of randomness, find the critical values from Table 10 of Appendix II.
(e) Conclude the test and interpret the results in the context of the application |
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| m102834 | Two plots at Rothamsted Experimental Station (see reference in Problem 5) were studied for production of wheat straw. For a random sample of years, the annual wheat straw production (in pounds) from one plot was as follows:
Use a calculator to verify that, for the preceding data, s2 ( 0.318.
Another random sample of years for a second plot gave the following annual wheat straw production (in pounds):
Use a calculator to verify that, for these data, s2 ( 1.078.
Test the claim that there is a difference (either way) in the population variance of wheat straw production for these two plots. Use a 5% level of signifi cance?
Please provide the following information.
(a) What is the level of signi ficance? State the null and alternate hypotheses.
(b) Find the value of the sample F statistic. What are the degrees of freedom?
What assumptions are you making about the original distribution?
(c) Find or estimate the P-value of the sample test statistic.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?
(e) Interpret your conclusion in the context of the application. |
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| m102835 | Two processes for manufacturing 60-watt light bulbs are under study. In both cases, the life (in hours) of the bulb before it burns out is being examined. A random sample of 18 light bulbs manufactured using the old process showed the sample variance of lifetimes to be s2 = 51.87. Another random sample of 16 light bulbs manufactured using the new process showed the sample variance of the lifetimes to be s2 = 135.24. Use a 5% level of significance to test the claim that the population variance of lifetimes for the new manufacturing process is larger than that of the old process. |
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| m102836 | Two processes for manufacturing large roller bearings are under study. In both cases, the diameters (in centimeters) are being examined. A random sample of 21 roller bearings from the old manufacturing process showed the sample variance of diameters to be s2 = 0.235. Another random sample of 26 roller bearings from the new manufacturing process showed the sample variance of their diameters to be s2 = 0.128. Use a 5% level of signi ficance to test the claim that there is a difference (either way) in the population variances between the old and new manufacturing processes. |
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| m102837 | Umbilical cord blood analysis immediately after delivery is one way to measure the health of an infant after birth. Researchers G. Natalucci et al. used it as a predictor of brain maturation of preterm infants in the article "Functional Brain Maturation Assessed During Early Life Correlates with Anatomical Brain Maturation at Term-Equivalent Age in Preterm Infants" (Pediatric Research, Vol. 74. No. 1, pp. 68-74). Based on this study, we will assume that, for preterm infants, the pH level of the arterial cord (one vessel in the umbilical cord) is normally distributed with mean 7.32 and standard deviation 0.1. Find the percentage of preterm infants who have arterial cord pH levels
a. Between 7.0 and 7.5.
b. Over 7.4. |
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| m102838 | Under the condition that both populations have equal standard deviations (σ1 - σ2), we can pool the standard deviations and use a Student s t distribution with degrees of freedom d.f. - n1 + n2 - 2 to fi nd the margin of error of a c confi dence interval for µ1 - µ2. This technique demonstrates another commonly used method of computing confi dence intervals for µ1 - µ2.
PROCEDURE
How to find a confidence interval for µ1 - µ2 when σ1 - σ2
Requirements
Consider two independent random samples, where
x̅1 and x̅2 are sample means from populations 1 and 2
s1 and s2 are sample standard deviations from populations 1 and 2
n1 and n2 are sample sizes from populations 1 and 2
If you can assume that both population distributions 1 and 2 are normal or at least mound-shaped and symmetric, then any sample sizes n1 and n2 will work.
If you cannot assume this, then use sample sizes n1 ≥ 30 and n2 ≥ 30.
Confidence interval for µ1 - µ2 when σ1 - σ2
Where
(pooled standard deviation)
c = confidence level (0 < c < 1)
tc - critical value for confi dence level c and degrees of freedom
d.f. = n1 + n2 - 2
With statistical software, select pooled variance or equal variance options.
(a) There are many situations in which we want to compare means from populations having standard deviations that are equal. The pooled standard deviation method applies even if the standard deviations are known to be only approximately equal. Consider Problem 23 regarding weights of gray |
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| m102839 | Under what circumstances is using a normal probability plot to assess the normality of a variable usually better than using a histogram, stem-and-leaf diagram, or dot-plot? |
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| m102840 | Under what three conditions are repeated trials of an experiment called Bernoulli trials? |
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| m102841 | "Unknown cultural affi liations and loss of identity at high elevations." These words are used to propose the hypothesis that archaeological sites tend to lose their identity as altitude extremes are reached. This idea is based on the notion that prehistoric people tended not to take trade wares to temporary settings and/or isolated areas (Source: Prehistoric New Mexico: Background for Survey, by D. E. Stuart and R. P. Gauthier, University of New Mexico Press). As elevation zones of prehistoric people (in what is now the state of New Mexico) increased, there seemed to be a loss of artifact identifi cation. Consider the following information.
Let p1 be the population proportion of unidentifi ed archaeological artifacts at the elevation zone 7000-7500 feet in the given archaeological area. Let p2 be the population proportion of unidenti fied archaeological artifacts at the elevation zone 5000-5500 feet in the given archaeological area.
(a) Check Requirements Can a normal distribution be used to approximate the 1 - 2 distribution? Explain.
(b) Find a 99% con fidence interval for p1 - p2.
(c) Interpretation Explain the meaning of the confi dence interval in the context of this problem. Does the confi dence interval contain all positive numbers? all negative numbers? both positive and negative numbers? What does this tell you (at the 99% con fidence level) about the comparison of the population proportion of unidenti fied artifacts at high elevations (7000-7500 feet) wi |
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| m102842 | USA Today reported that about 20% of all people in the United States are illiterate. Suppose you interview seven people at random off a city street.
(a) Make a histogram showing the probability distribution of the number of illiterate people out of the seven people in the sample.
(b) Find the mean and standard deviation of this probability distribution. Find the expected number of people in this sample who are illiterate.
(c) How many people would you need to interview to be 98% sure that at least seven of these people can read and write (are not illiterate)? |
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| m102843 | USA Today reported that for all airlines, the number of lost bags was
May: 6.02 per 1000 passengers December: 12.78 per 1000 passengers
Note: A passenger could lose more than one bag.
(a) Let r = number of bags lost per 1000 passengers in May. Explain why the Poisson distribution would be a good choice for the random variable r. What is ( to the nearest tenth?
(b) In the month of May, what is the probability that out of 1000 passengers, no bags are lost? that 3 or more bags are lost? that 6 or more bags are lost?
(c) In the month of December, what is the probability that out of 1000 passengers, no bags are lost? that 6 or more bags are lost? that 12 or more bags are lost? (Round l to the nearest whole number.) |
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| m102844 | USA Today reported that Park eld, California, is dubbed the world s earthquake capital because it sits on top of the notorious San Andreas fault. Since 1857, Park eld has had a major earthquake on the average of once every 22 years.
(a) Explain why a Poisson probability distribution would be a good choice for r = number of earthquakes in a given time interval.
(b) Compute the probability of at least one major earthquake in the next 22 years. Round l to the nearest hundredth, and use a calculator.
(c) Compute the probability that there will be no major earthquake in the next 22 years. Round l to the nearest hundredth, and use a calculator.
(d) Compute the probability of at least one major earthquake in the next 50 years. Round l to the nearest hundredth, and use a calculator.
(e) Compute the probability of no major earthquakes in the next 50 years. Round ( to the nearest hundredth, and use a calculator. |
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| m102845 | USA Today reported that the U.S. (annual) birthrate is about 16 per 1000 people, and the death rate is about 8 per 1000 people.
(a) Explain why the Poisson probability distribution would be a good choice for the random variable r = number of births (or deaths) for a community of a given population size.
(b) In a community of 1000 people, what is the (annual) probability of 10 births? What is the probability of 10 deaths? What is the probability of 16 births? 16 deaths?
(c) Repeat part (b) for a community of 1500 people. You will need to use a calculator to compute P(10 births) and P(16 births).
(d) Repeat part (b) for a community of 750 people. |
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| m102846 | USA Today reports that about 25% of all prison parolees become repeat offenders. Alice is a social worker whose job is to counsel people on parole. Let us say success means a person does not become a repeat offender. Alice has been given a group of four parolees.
(a) Find the probability P(r) of r successes ranging from 0 to 4.
(b) Make a histogram for the probability distribution of part (a).
(c) What is the expected number of parolees in Alice s group who will not be repeat offenders? What is the standard deviation?
(d) How large a group should Alice counsel to be about 98% sure that three or more parolees will not become repeat offenders? |
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| m102847 | USA Today reports that the average expenditure on Valentine s Day is $100.89. Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 40 male consumers was $135.67, and the average expenditure in a sample survey of 30 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $35, and the standard deviation for female consumers is assumed to be $20.
a. What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females?
b. At 99% confidence, what is the margin of error?
c. Develop a 99% confidence interval for the difference between the two population means. |
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| m102848 | Use cutpoint grouping with a first class midpoint of 0.5 and a class width of 1.
a. Determine a frequency distribution.
b. Obtain a relative-frequency distribution.
c. Construct a frequency histogram based on your result from part (a).
d. Construct a relative-frequency histogram based on your result from part (b). |
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| m102849 | Use cutpoint grouping with a first class of 10-under 15.
a. Determine a frequency distribution.
b. Obtain a relative-frequency distribution.
c. Construct a frequency histogram based on your result from part (a).
d. Construct a relative-frequency histogram based on your result from part (b). |
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