New Semester
Started
Get
50% OFF
Study Help!
--h --m --s
Claim Now
Question Answers
Textbooks
Find textbooks, questions and answers
Oops, something went wrong!
Change your search query and then try again
S
Books
FREE
Study Help
Expert Questions
Accounting
General Management
Mathematics
Finance
Organizational Behaviour
Law
Physics
Operating System
Management Leadership
Sociology
Programming
Marketing
Database
Computer Network
Economics
Textbooks Solutions
Accounting
Managerial Accounting
Management Leadership
Cost Accounting
Statistics
Business Law
Corporate Finance
Finance
Economics
Auditing
Tutors
Online Tutors
Find a Tutor
Hire a Tutor
Become a Tutor
AI Tutor
AI Study Planner
NEW
Sell Books
Search
Search
Sign In
Register
study help
mathematics
calculus
Modeling the Dynamics of Life Calculus and Probability for Life Scientists 3rd edition Frederick R. Adler - Solutions
Use the method of support to estimate 95% confidence limits and compare your results with Exercise 35. Consider a data set where three out of three people are found with an allele.
A person wins the lottery the fifth time he plays. Does the value q = 0.001 for the probability of success lie within the 99% confidence limits? In the above situation, find the probability of a result as extreme as or more extreme than the actual result for the given value of the parameter.
Find the 95% confidence limits. A person places an advertisement to sell his car in the newspaper and settles down to await calls, which he expects will arrive with an exponential distribution. The first call arrives in 20 min.
Find the 98% confidence limits. A person places an advertisement to sell his car in the newspaper and settles down to await calls, which he expects will arrive with an exponential distribution. The first call arrives in 20 min.
How many calls might he expect to miss if he went out for a 2-h hike? A person places an advertisement to sell his car in the newspaper and settles down to await calls, which he expects will arrive with an exponential distribution. The first call arrives in 20 min.
Write the equations for the 95% confidence limits, and solve them numerically if you have a computer. 14 mutations are counted in one million base pairs.
Write the equations for the approximate 95% confidence limits using the method of support, and solve them numerically if you have a computer. 14 mutations are counted in one million base pairs.
Find 95% confidence limits around the maximum likelihood estimate of q. How do you interpret these results? Recall the couple that has seven boys before having a girl (Section 8.1, Exercise 33).
Find 99% confidence limits around the maximum likelihood estimate of q. How do you interpret these results? Recall the couple that has seven boys before having a girl (Section 8.1, Exercise 33).
Three cosmic rays hit a detector in 1 yr. Does the value λ = 10.0 for the rate at which rays hit lie within the 98% confidence limits? In the above situation, find the probability of a result as extreme as or more extreme than the actual result for the given value of the parameter.
One cosmic ray hits a detector in 1 yr. Does the value λ = 5.0 for the rate at which rays hit lie within the 98% confidence limits? In the above situation, find the probability of a result as extreme as or more extreme than the actual result for the given value of the parameter.
Find the 95% confidence limits if a coin is flipped five times and comes up heads every time (Exercise 1). Find the exact confidence limits and check if the value for the earlier problem lies within them.
Find the 95% confidence limits if a coin is flipped seven times and comes up heads six out of seven times (Exercise 2). Find the exact confidence limits and check if the value for the earlier problem lies within them.
Find the 99% confidence limits if a person wins the lottery the second time he plays (Exercise 3). Find the exact confidence limits and check if the value for the earlier problem lies within them.
The weight W. Consider the following data on 20 plants.Find the following for the given measurement. a. The sample mean. b. The sample median. c. The trimmed means tr(5), tr(10), and tr(20).
Find how many measurements lie (a) less than one sample standard deviation from the sample mean and (b) more than two sample standard deviations from the sample mean for the given measurement. Which behave more or less like the normal distribution?For Information: The height H in Exercise 2.
Find how many measurements lie (a) less than one sample standard deviation from the sample mean and (b) more than two sample standard deviations from the sample mean for the given measurement. Which behave more or less like the normal distribution?For Information: The yield Y in Exercise 3.
Find how many measurements lie (a) less than one sample standard deviation from the sample mean and (b) more than two sample standard deviations from the sample mean for the given measurement. Which behave more or less like the normal distribution?For information: The seed number S in Exercise 4.
Find the 95% confidence limits around the sample mean for the given measurement, assuming that the sample variance s is a good estimate of the true variance σ.1. The weight W in Exercises 1 and 5.2. The height H in Exercises 2 and 6.3. The yield Y in Exercises 3 and 7.4. The seed number S in
Find the 95% confidence limits around the sample mean for the given measurement, without assuming that the sample variance s is a good estimate of the true variance σ (thus using the t distribution).1. The weight W in Exercises 1 and 5.2. The height H in Exercises 2 and 6.3. The yield Y in
The height H. Consider the following data on 20 plants.Find the following for the given measurement.a. The sample mean.b. The sample median.c. The trimmed means tr(5), tr(10), and tr(20).
98% confidence limits around the weight W in Exercise 1. Find the given confidence limits around the sample mean for the given measurement, assuming that the sample variance s is a good estimate of the true variance σ.
90% confidence limits around the height H in Exercise 2. Find the given confidence limits around the sample mean for the given measurement, assuming that the sample variance s is a good estimate of the true variance σ.
99.8% confidence limits around the yield Y in Exercise 3. Find the given confidence limits around the sample mean for the given measurement, assuming that the sample variance s is a good estimate of the true variance σ.
99.9% confidence limits around the seed number S in Exercise 4. Find the given confidence limits around the sample mean for the given measurement, assuming that the sample variance s is a good estimate of the true variance σ.
Find the normal approximation to the following.1. The average of 30 numbers chosen from the exponential p.d.f. g(x) = 2e-2x.2. The average of 30 numbers chosen from the p.d.f. f(x) = 1 for 0 ≤ x ≤ 1.
Find 95% confidence intervals in the following cases, assuming that the standard deviations are known to match those in the earlier problem. Does the confidence interval include the true mean?1. A sample mean of 0.4 is found in Exercise 25.2. A sample mean of 0.7 is found in Exercise 26.
A coin is flipped 100 times and comes out heads 44 times.Use the normal approximation to find 95% confidence limits around the estimated proportion in the above case.
The yield Y. Consider the following data on 20 plants.Find the following for the given measurement. a. The sample mean. b. The sample median. c. The trimmed means tr(5), tr(10), and tr(20).
Of 1000 people polled, 320 favor the use of mathematics in biology.Use the normal approximation to find 95% confidence limits around the estimated proportion in the above case.
The 99% confidence limits with the normal distribution. The 95% confidence limits with the t distribution are wider than those with the normal distribution. For approximately how many degrees of freedom do they match the given confidence limits with the normal distribution? How large a sample does
The 98% confidence limits with the normal distribution. The 95% confidence limits with the t distribution are wider than those with the normal distribution. For approximately how many degrees of freedom do they match the given confidence limits with the normal distribution? How large a sample does
Find the mean squared deviation from the mean for each and average them to find the expected sample variance. In simple cases, we can see why using a denominator of n in the equation for the sample variance produces a biased estimate. Suppose a population consists of half 0 s and half 1 s.
Compare with the true answer and show that using a denominator of n - 1 rather than n would give the right answer. Try to explain the bias. In simple cases, we can see why using a denominator of n in the equation for the sample variance produces a biased estimate. Suppose a population consists of
Population a.Consider the following data on immigration into four populations over 20 yr. For each, find the sample mean and the sample standard deviation. Compare them with the mathematical mean and standard deviation found in the earlier problem.For Information: (see Section 7.8, Exercise 33)
Population b.Consider the following data on immigration into four populations over 20 yr. For each, find the sample mean and the sample standard deviation. Compare them with the mathematical mean and standard deviation found in the earlier problem.For Information: (see Section 7.8, Exercise 34)
Population c. Why are the mean and variance so different from the mathematical expectations?Consider the following data on immigration into four populations over 20 yr. For each, find the sample mean and the sample standard deviation. Compare them with the mathematical mean and standard deviation
The seed number S. Consider the following data on 20 plants.Find the following for the given measurement. a. The sample mean. b. The sample median. c. The trimmed means tr(5), tr(10), and tr(20).
Population d.Consider the following data on immigration into four populations over 20 yr. For each, find the sample mean and the sample standard deviation. Compare them with the mathematical mean and standard deviation found in the earlier problem.For Information: (see Section 7.8, Exercise 36)
Population a. Find the 95% confidence intervals around the mean number of immigrants using both the true variance and the sample variance. Does the true mean lie within the confidence limits?
Population b. Find the 95% confidence intervals around the mean number of immigrants using both the true variance and the sample variance. Does the true mean lie within the confidence limits?
Population c. Find the 95% confidence intervals around the mean number of immigrants using both the true variance and the sample variance. Does the true mean lie within the confidence limits?
Population d. Find the 95% confidence intervals around the mean number of immigrants using both the true variance and the sample variance. Does the true mean lie within the confidence limits?
Of 50 offspring, 35 are tall.Several plants are crossed, producing the following proportions. Find 99% confidence limits around the fraction of tall plants in each case.
Of 500 offspring, 350 are tall.Several plants are crossed, producing the following proportions. Find 99% confidence limits around the fraction of tall plants in each case.
Of 100 offspring, 52 are tall.Several plants are crossed, producing the following proportions. Find 99% confidence limits around the fraction of tall plants in each case.
Of 200 offspring, 13 are tall.Several plants are crossed, producing the following proportions. Find 99% confidence limits around the fraction of tall plants in each case.
Use the normal approximation to the Poisson distribution to estimate 95% confidence limits around the true mean number of mutations per million base pairs and compare with Section 8.2, Exercise 43. Mutations are counted in a large section of the genome. This count finds 14 mutations in one set of 1
Find the sample variance, the sample standard deviation, and the standard error for the given measurement.1. The weight W in Exercise 1.2. The height H in Exercise 2.3. The yield Y in Exercise 3.4. The seed number S in Exercise 4.
Thirty different sets of 1 million base pairs are measured, and the average number of mutations per million is found to be 13.5. Estimate the standard deviation, and find the standard error of the mean and the 99% confidence limits. Mutations are counted in a large section of the genome. This count
Find how many measurements lie (a) less than one sample standard deviation from the sample mean and (b) more than two sample standard deviations from the sample mean for the given measurement. Which behave more or less like the normal distribution?For Information: The weight W in Exercise 1.
The p-value associated with the null hypothesis is 0.2. Explain in words what the above statement mean, and restate the result in terms of type I or type II errors as appropriate.
What is the cutoff number of heads above which you reject the null hypothesis at the α = 0.1 significance level? A coin is flipped 10 times and comes up heads 9 times. You have reason to suspect however, that the coin produces an excess of heads (and have told this to a friend in advance), as in
One cosmic ray hits a detector in 1 yr. The null hypothesis is that the rate at which rays hit is λ = 5/yr. Find the p-value with both one-tailed and a two-tailed tests.
Three cosmic rays hit a larger detector in 1 yr. The null hypothesis is that the rate at which rays hit is λ = 10/yr. Find the p-value with both one-tailed and a two-tailed tests.
You wait 4000 h for an exponentially distributed event to occur. The null hypothesis is that the mean wait is 1000 h with the alternative hypothesis that the mean wait is greater than 1000 h. Find the p-value associated with the above hypotheses.
You wait 40 h for an exponentially distributed event to occur. The null hypothesis is that the mean wait is 1000 h with the alternative hypothesis that the mean wait is less than 1000 h. Find the p-value associated with the above hypotheses.
The first defective gasket is the 25th. The null hypothesis is that the first defect follows a geometric distribution with mean 10, and the alternative hypothesis is that the mean is greater than 10. Find the p-value associated with the above hypotheses.
The first defective gasket is the 50th. The null hypothesis is that the first defect follows a geometric distribution with mean 1000, and the alternative hypothesis is that the mean is less than 1000. Find the p-value associated with the above hypotheses.
Certain screens for cancer work by examining many cells under a microscope and looking for abnormalities. Discuss how setting the threshold for cell abnormality can affect the number of type I and type II errors. What factors would go into deciding where to set the threshold? Think about how
Out of 1000 simulations of the null hypothesis, 70 produce a result as extreme as or more extreme than the actual observation. Explain in words what the above statement mean, and restate the result in terms of type I or type II errors as appropriate.
Certain screens for cancer drugs work by examining many drugs and looking for those that suppress tumor growth. Discuss how setting the threshold for tumor growth reduction can affect the number of type I and type II errors. What factors would go into deciding where to set the threshold? Think
Test the hypothesis that boys and girls are equally likely. Consider a couple that has seven boys and one girl in a family of eight.
At birth, boys are slightly more common than girls. Test the hypothesis that 55% of births are boys. Consider a couple that has seven boys and one girl in a family of eight
You receive 7 calls in 1 h on the first day. Phone calls used to arrive at an average rate of 3.5/h, but after posting your number on your Web page, you receive more calls on subsequent days. For each day, a. State null and alternative hypotheses. b. Use the Poisson distribution to compute the
You receive 8 calls in 1 hr on the second day. Phone calls used to arrive at an average rate of 3.5/h, but after posting your number on your Web page, you receive more calls on subsequent days. For each day, a. State null and alternative hypotheses. b. Use the Poisson distribution to compute the
Find the cutoff value for a test with α = 0.05. Find the power with λ = 4.0, λ = 7.0, and λ = 10.0. Explain why the power is higher for larger values of Λ. Consider the data in Exercise 23, where calls arrive at a rate of 3.5/h before posting your phone number on your Web page, but 7 arrive in
Find the cutoff value for a test with α = 0.01. Find the power with λ = 4.0, λ = 7.0, and λ = 10.0. Why does a higher significance level reduce the power? Consider the data in Exercise 23, where calls arrive at a rate of 3.5/h before posting your phone number on your Web page, but 7 arrive in 1
State null and alternative hypotheses for the first type of cell. At what level can you reject the null hypothesis? Is it significant? The survival time for one type of cell in culture is exponentially distributed with a mean of 200 h. After applying a new treatment, one cell lasts 800 h. For a
State null and alternative hypotheses for the second type of cell. At what level can you reject the null hypothesis? Is it significant? The survival time for one type of cell in culture is exponentially distributed with a mean of 200 h. After applying a new treatment, one cell lasts 800 h. For a
Suppose you adopt the cutoff from Exercise 29. Find and graph the power as a function of the true mean. What is the power of the test if the true mean is 500? What is the power of the test if the true mean is 1000? The survival time for one type of cell in culture is exponentially distributed with
Suppose you adopt the cutoff from Exercise 30. Find and graph the power as a function of the true mean. What is the power of the test if the true mean is 50? What is the power of the test if the true mean is 10? The survival time for one type of cell in culture is exponentially distributed with a
Solve for the smallest value of the mean for which the power to detect an improvement in cells of the first type is equal to 0.95. Interpret your answer. The survival time for one type of cell in culture is exponentially distributed with a mean of 200 h. After applying a new treatment, one cell
Solve for the largest value of the mean for which the power to detect harm to cells of the second type is equal to 0.95. Interpret your answer. The survival time for one type of cell in culture is exponentially distributed with a mean of 200 h. After applying a new treatment, one cell lasts 800 h.
95% confidence limits where the upper and lower confidence limits are 1.0 cm from the sample mean. Consider measuring n plants with a known standard deviation of 3.2 cm. How many plants would have to be measured to achieve the above?
99% confidence limits where the upper and lower confidence limits are 1.0 cm from the sample mean. Consider measuring n plants with a known standard deviation of 3.2 cm. How many plants would have to be measured to achieve the above?
A coin is flipped 5 times and comes up heads every time. Using the above data, find the p-value associated with the null hypothesis that the true probability of heads is 0.5. Is the result significant?
A coin is flipped 7 times and comes up heads 6 out of 7 times. Using the above data, find the p-value associated with the null hypothesis that the true probability of heads is 0.5. Is the result significant?
A coin is flipped 10 times and comes up heads 9 times. You have reason to suspect however, that the coin produces an excess of heads (and have told this to a friend in advance). Using the above data, find the p-value associated with the null hypothesis that the true probability of heads is 0.5. Is
A coin is flipped 20 times and comes up heads 3 times. You have reason to suspect however, that the coin produces an excess of tails (and have told this to a friend in advance). Using the above data, find the p-value associated with the null hypothesis that the true probability of heads is 0.5. Is
What is the cutoff number of heads above which you reject the null hypothesis at the α = 0.05 significance level? A coin is flipped 10 times and comes up heads 9 times. You have reason to suspect however, that the coin produces an excess of heads (and have told this to a friend in advance), as in
The variance for weight is 9.0, and plants outside the plot have mean weight 10.0.The weights, heights, yields, and seed number for 10 plants grown in an experimental plot are given in the table. Each measurement is approximately normally distributed. We wish to determine whether plants in the plot
Under the conditions in Exercise 4, find the smallest seed number that can reject the null hypothesis that the mean seed number is 15.0 with a one-tailed test at the 0.001 level. Find the smallest values of the sample mean for which the given hypothesis is rejected.
The true mean weight is 13.0 in Exercise 9. Find the power of the test assuming the given true mean.
The true mean seed height is 18.0 in Exercise 12. Find the power of the test assuming the given true mean.
Consider again plants with the null hypothesis that mean height is 39.0. Assume that the standard deviation is known to be 3.2 cm.1. Show that a measured sample mean of 40.0 is highly significant if the sample size is n = 88.2. Why is the power with this sample size only 90% (as found in the text),
A coin is flipped 100 times and comes out heads 44 times. It is thought that the coin is fair (has probability of heads is equal to 0.5). Do the data provide evidence that the coin is unfair? Use the normal approximation to test the given hypothesis.
The variance for height is 16.0, and plants outside the plot have mean height 38.0.The weights, heights, yields, and seed number for 10 plants grown in an experimental plot are given in the table. Each measurement is approximately normally distributed. We wish to determine whether plants in the
Of 1000 people polled in one state, 320 favor the use of mathematics in biology. The legislature has passed a bill mandating that at least 36% of people must be in favor. Does the poll provide evidence that the proportion is smaller than 0.36? Is the state in violation of the law? Use the normal
Find the p-value associated with the null hypothesis that the mean of type a is 1.0.Consider the following data on 30 waiting times for 2 types of events.
Find the p-value associated with the null hypothesis that the mean of type b is 1.0.Consider the following data on 30 waiting times for 2 types of events.
The outlier is extreme value 6.33 at time 16.Consider again the data in Exercises 21 and 22. Each type has one or more outliers that strongly affect the mean and standard deviation. Exclude the outlier or outliers and recompute the p-value associated with the null hypothesis that the mean is 1.0.
The outliers are the extreme values 4.16 and 4.83.Consider again the data in Exercises 21 and 22. Each type has one or more outliers that strongly affect the mean and standard deviation. Exclude the outlier or outliers and recompute the p-value associated with the null hypothesis that the mean is
Of 25 of 50 patients tested with the new medication, 30 improve. Is this significant? A chronic condition improves spontaneously in 45% of people. A new medication is being tested to try to increase this percentage.
Of 26 of 100 patients tested with the new medication, 60 improve. Is this significantly better? A chronic condition improves spontaneously in 45% of people. A new medication is being tested to try to increase this percentage.
Suppose that the true fraction that improves with the medication is 0.6. What is the power to detect this at the 0.05 level with a sample of 50 patients? A chronic condition improves spontaneously in 45% of people. A new medication is being tested to try to increase this percentage.
Suppose that the true fraction that improves with the medication is 0.6. What is the power to detect this at the 0.05 level with a sample of 100 patients? How much greater is the power? A chronic condition improves spontaneously in 45% of people. A new medication is being tested to try to increase
Find the significance level if the DNA with the new method has only 27 errors. Make sure to start by finding the normal approximation to the null hypothesis. A company develops a new method to reduce error rates in the polymerase chain reaction (PCR). With the old method, the number of errors in a
The variance for yield is 6.25, and plants outside the plot have mean yield 9.0.The weights, heights, yields, and seed number for 10 plants grown in an experimental plot are given in the table. Each measurement is approximately normally distributed. We wish to determine whether plants in the plot
Find the significance level if the DNA with the new method has only 23 errors. A company develops a new method to reduce error rates in the polymerase chain reaction (PCR). With the old method, the number of errors in a well-studied piece of DNA is known to have a Poisson distribution with mean
Showing 5700 - 5800
of 14230
First
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
Last
Step by Step Answers
Get 50% OFF
Claim Now
.png)
.png)
.png)
.png)
.png)
.png)
.png)
.png)
.png)
.png)
.png)
.png)
.png)
.png)
.png)
.png)
.png)
.png)
.png)
.png)
.png)
.png)
