8.7.1 Suppose that the number N of molecules of toxin left in a cell after 10.0 min is thought to follow the probability distribution with Pr(N = 0) = 0.4, Pr(N = 1) = 0.3, Pr(N = 2) = 0.2, and Pr(N = 3) = 0.1
(as in Example 6.3.11). Test whether the following data fit the
expectation from this extrinsic hypothesis. There are 35 cells with no
molecules, 25 with one molecule, 25 with two molecules, and 15 with
three molecules.
Get solution
8.7.2 Suppose that the number N of molecules of toxin left in a cell after 10.0 min is thought to follow the probability distribution with Pr(N = 0) = 0.4, Pr(N = 1) = 0.3, Pr(N = 2) = 0.2, and Pr(N = 3) = 0.1
(as in Example 6.3.11). Test whether the following data fit the
expectation from this extrinsic hypothesis. There are 25 cells with no
molecules, 21 with one molecule, 19 with two molecules, and 15 with
three molecules.
Get solution
8.7.4 Suppose that the number N of molecules of toxin left in a cell after 10.0 min is thought to follow the probability distribution with Pr(N = 0) = 0.4, Pr(N = 1) = 0.3, Pr(N = 2) = 0.2, and Pr(N = 3) = 0.1 (as in Example 6.3.11). Test whether the following data fit the expectation from this extrinsic hypothesis. Consider
again the data in Exercise 2, but suppose that we can only distinguish
cells with no molecules from those with at least one. Find how many
cells are in each of these two categories and compare with the
appropriate extrinsic hypothesis. Why might the test give a different
result than with the unpooled data?
Get solution
8.7.4 Suppose that the number N of molecules of toxin left in a cell after 10.0 min is thought to follow the probability distribution with Pr(N = 0) = 0.4, Pr(N = 1) = 0.3, Pr(N = 2) = 0.2, and Pr(N = 3) = 0.1 (as in Example 6.3.11). Test whether the following data fit the expectation from this extrinsic hypothesis. Consider
again the data in Exercise 2, but suppose that we can only distinguish
cells with no molecules from those with at least one. Find how many
cells are in each of these two categories and compare with the
appropriate extrinsic hypothesis. Why might the test give a different
result than with the unpooled data?
Get solution
8.7.5 The
number of molecules remaining in a cell is thought to follow a binomial
distribution with the given parameter. In each case, find whether there
is reason to reject this model. Suppose there are three molecules, and that the probability of remaining is thought to be p = 0.6. In a sample of 80 cells, we find 10 with 0 molecules, 20 with 1 molecule, 30 with 2 molecules, and 20 with 3 molecules.
Get solution
8.7.6
The
number of molecules remaining in a cell is thought to follow a binomial
distribution with the given parameter. In each case, find whether there
is reason to reject this model. Suppose there are 4 molecules, and
that the probability of a molecule’s remaining is thought to be p = 0.6.
In a sample of 80 cells, we find 5 with no molecules, 20 with one
molecule, 20 with two molecules, 20 with three molecules, and 15 with
four molecules.
Get solution
8.7.7 Compute the statistic ... in the earlier exercise using the continuity correction. Does it alter the conclusions? The situation in Exercise 5.
Get solution
8.7.8 Compute the statistic ... in the earlier exercise using the continuity correction. Does it alter the conclusions? The situation in Exercise 6.
Get solution
8.7.9 Suppose
that the data in Exercises 5 and 6 are thought to follow a binomial
distribution with an unknown parameter. Estimate this parameter and test
whether the data fit the resulting model. The situation in Exercise 5.
Get solution
8.7.10 Suppose
that the data in Exercises 5 and 6 are thought to follow a binomial
distribution with an unknown parameter. Estimate this parameter and test
whether the data fit the resulting model. The situation in Exercise 6.
Get solution
8.7.11
Consider the following data, which were supposedly generated from 200
replicates of a Poisson process. ... Test the extrinsic
hypothesis that Λ= 4.5 for experiment 1.
Get solution
8.7.12
Consider the following data, which were supposedly generated from 200
replicates of a Poisson process. ... Test the extrinsic
hypothesis that Λ = 4.0 for experiment 2
Get solution
8.7.13
Consider the following data, which were supposedly generated from 200
replicates of a Poisson process. ... Test the intrinsic
hypothesis that the data follow a Poisson distribution for experiment 1.
Get solution
8.7.15
Consider again the data on mites and lice from Example 8.7.14.
... Find the probabilities for each term in the table, and find the
conditional distributions. The
distribution of the number of lice conditional on 0, 1, and 2 mites.
How different are the conditional distributions, and would they lead you
to suspect that the two pests do not act independently?
Get solution
8.7.15
Consider again the data on mites and lice from Example 8.7.14.
... Find the probabilities for each term in the table, and find the
conditional distributions. The
distribution of the number of lice conditional on 0, 1, and 2 mites.
How different are the conditional distributions, and would they lead you
to suspect that the two pests do not act independently?
Get solution
8.7.16
Consider again the data on mites and lice from Example 8.7.14.
... Find the probabilities for each term in the table, and find the
conditional distributions. The
distribution of the number of mites conditional on 0, 1, and 2 lice.
How different are the conditional distributions, and would they lead you
to suspect that the two pests do not act independently?
Get solution
8.7.17
Test the following tables for independence. Consider the following
data on mating in birds. ... Do matings deviate from
independence, and what might it mean?
Get solution
8.7.18
Test the following tables for independence. Consider the following
data on student class attendance. ... Is attendance independent,
and if not, what might it mean?
Get solution
8.7.19 The significance of deviations from the null hypothesis depends on the sample size. Conduct a ...
test for the following samples based on Example 8.7.1. Suppose that 20%
of diseased people tested have a particular allele (this would, of
course, vary in a series of real experiments), and that 13% of healthy
people are known to have the allele. Suppose we tested only 50
diseased people. Find the significance of the result and compare to the
results with a sample size of 100.
Get solution
8.7.20 The significance of deviations from the null hypothesis depends on the sample size. Conduct a ...
test for the following samples based on Example 8.7.1. Suppose that 20%
of diseased people tested have a particular allele (this would, of
course, vary in a series of real experiments), and that 13% of healthy
people are known to have the allele. Suppose we tested 200 diseased
people. Find the significance and compare to the results with a sample
size of 100.
Get solution
8.7.21 The significance of deviations from the null hypothesis depends on the sample size. Conduct a ...
test for the following samples based on Example 8.7.1. Suppose that 20%
of diseased people tested have a particular allele (this would, of
course, vary in a series of real experiments), and that 13% of healthy
people are known to have the allele. Suppose we tested n diseased people. Compute ... as a function of n. Does it increase proportionally to the sample size?
Get solution
8.7.22 The significance of deviations from the null hypothesis depends on the sample size. Conduct a ...
test for the following samples based on Example 8.7.1. Suppose that 20%
of diseased people tested have a particular allele (this would, of
course, vary in a series of real experiments), and that 13% of healthy
people are known to have the allele. Suppose we tested n diseased people. How many people would we need to test to find a result significant at the 0.01 level?
Get solution
8.7.23 A random variable ...follows a ... distribution with ν degrees of freedom if ... where ...follow the standard normal distribution. Find the expectation of ....
Get solution
8.7.24 A random variable ...follows a ... distribution with ν degrees of freedom if ... where ...follow the standard normal distribution. Find the expectation of ... .
Get solution
8.7.25 A random variable ...follows a ... distribution with ν degrees of freedom if ... where ...follow the standard normal distribution. Compute the critical value for p = 0.05 with 1 degree of freedom.
Get solution
8.7.26 A random variable ...follows a ... distribution with ν degrees of freedom if ... where ...follow the standard normal distribution. Remarkably enough, ...
is an exponential distribution. Using the mean found in Exercise 24,
find the parameter of this distribution, and compute the critical value
for p = 0.05.
Get solution
8.7.27 Use the ...test
to check whether the control and treatment differ in the following
contingency tables. Consider the following data on the behavior of 50
wild type and 100 mutant worms. ...
Get solution
8.7.28 Use the ...test
to check whether the control and treatment differ in the following
contingency tables. Consider the following data on the behavior of 100
wild type and 150 mutant worms. ...
Get solution
8.7.29 Use the ...test
to check whether the control and treatment differ in the following
contingency tables. Consider the following data on the behavior of 80
wild type and 120 mutant worms. ...
Get solution
8.7.30 Use the ...test
to check whether the control and treatment differ in the following
contingency tables. Consider the following data on the behavior of 100
wild type and 125 mutant worms. ...
Get solution
8.7.31 A
recessive allele is expected to be expressed in 25% of offspring from a
cross of heterozygous plants. Check whether the following data are
consistent with this hypothesis. Ten out of 60 plants are homozygous for the recessive allele.
Get solution
8.7.32 A
recessive allele is expected to be expressed in 25% of offspring from a
cross of heterozygous plants. Check whether the following data are
consistent with this hypothesis. Twenty-one out of 120 plants are homozygous for the recessive allele.
Get solution
8.7.33
Suppose that plants with genotype WW have white flowers, those with
genotype WR or RW have pink flowers, and those with genotype RR have red
flowers. Two RW plants are crossed. Check whether the following data
are consistent with the expected ratios. If not, try to explain why.
Out of 90 offspring, there are 18 white, 40 pink, and 32 red.
Get solution
8.7.34
Suppose that plants with genotype WW have white flowers, those with
genotype WR or RW have pink flowers, and those with genotype RR have red
flowers. Two RW plants are crossed. Check whether the following data
are consistent with the expected ratios. If not, try to explain why.
Suppose 10 additional plants had been measured in Exercise 33, and there
were 3 pink ones and 7 red ones.
Get solution
8.7.35 Suppose
two traits are controlled by two unlinked loci (so the phenotypes are
independent), one for flower color and one for height. Check whether the
following data are consistent with the expected numbers in the
following scenarios. Suppose that both yellow flower color and
shortness are recessive, with white flower color and tallness expressed
in the dominant plants. Two parents that are heterozygous for these two
traits are crossed, and 80 offspring are checked. Of these, 3 have
yellow flowers and are short, 12 have yellow flowers and are tall, 17
have white flowers and are short, and 48 have white flowers and are
tall.
Get solution
8.7.36 Suppose
two traits are controlled by two unlinked loci (so the phenotypes are
independent), one for flower color and one for height. Check whether the
following data are consistent with the expected numbers in the
following scenarios. Suppose that both yellow flower color and
shortness are recessive, with white flower color and tallness expressed
in the dominant plants. Two parents that are heterozygous for these two
traits are crossed, and 87 offspring are checked. Of these, 11 have
yellow flowers and are short, 8 have yellow flowers and are tall, 13
have white flowers and are short, and 55 have white flowers and are
tall.
Get solution
8.7.37 An
ecologist counts the numbers of jack rabbits and eagles observed, and
wishes to know whether they are independent (as in Section 6.4,
Exercises 27 and 28). E represents the number of eagles seen, and J the number of jackrabbits. Use the ...
test to check. Eighty counts are made, with the following results.
... Are the results significant? Compare with Section 7.1,
Get solution
8.7.38 An
ecologist counts the numbers of jack rabbits and eagles observed, and
wishes to know whether they are independent (as in Section 6.4,
Exercises 27 and 28). E represents the number of eagles seen, and J the number of jackrabbits. Use the ...
test to check. Eighty counts are made, with the following results.
... Are the results significant? Compare with Section 7.1, Exercise
28.
Get solution
8.7.39 Recall
the falcon data studied in Example 8.7.15, where 44 families of two
birds were studied, and 14 had no males, 14 had one male, and 16 had 2
males. However, now assume that the order of birth is taken into
account, so that there are four possible families (the first offspring
could be male or female as could the second). Write a table and evaluate
for lack of independence in the following cases, and compare with the
results in Example 8.7.15. Of the 14 females with one male, 7 had a male first.
Get solution
8.7.40 Recall
the falcon data studied in Example 8.7.15, where 44 families of two
birds were studied, and 14 had no males, 14 had one male, and 16 had 2
males. However, now assume that the order of birth is taken into
account, so that there are four possible families (the first offspring
could be male or female as could the second). Write a table and evaluate
for lack of independence in the following cases, and compare with the
results in Example 8.7.15. Of the 14 females with one male, 3 had a male first.
Get solution
