8.8.1 Using the following data, use the method of support to
evaluate the null hypothesis that the true probability of heads is 0.5.
A coin is flipped 5 times and comes up heads every time (as in Section
8.4, Exercise 5).
Get solution
8.8.2
Using the following data, use the method of support to evaluate the
null hypothesis that the true probability of heads is 0.5. A coin is
flipped 7 times and comes up heads 6 out of 7 times (as in Section 8.4,
Exercise 6).
Get solution
8.8.3
Using the following data, use the method of support to evaluate the
null hypothesis that the true probability of heads is 0.5. A coin is
flipped 10 times and comes up heads 9 times (as in Section 8.4, Exercise
7).
Get solution
8.8.4
Using the following data, use the method of support to evaluate the
null hypothesis that the true probability of heads is 0.5. A coin is
flipped 20 times and comes up heads 3 times (as in Section 8.4, Exercise
8).
Get solution
8.8.5
Use the method of support to evaluate the following null hypotheses.
One cosmic ray hits a detector in 1 yr. The null hypothesis is that the
rate at which rays hit is λ= 5/yr (as in Section 8.4, Exercise 13.)
Get solution
8.8.6
Use the method of support to evaluate the following null hypotheses.
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 (as in Section 8.4, Exercise 14.)
Get solution
8.8.7 Find the difference in support of the following hypotheses. Compare with the p-value in the earlier problem. You
wait 4000 h for an exponentially distributed event to occur. The null
hypothesis is that the mean wait is 1000 h with alternative that the
mean wait is greater than 1000 h (as in Section 8.4, Exercise 15).
Get solution
8.8.8 Find the difference in support of the following hypotheses. Compare with the p-value in the earlier problem. You
wait 40 h for an exponentially distributed event to occur. The null
hypothesis is that the mean wait is 1000 h with alternative that the
mean wait is less than 1000 h (as in Section 8.4, Exercise 16).
Get solution
8.8.9 Find the difference in support of the following hypotheses. Compare with the p-value in the earlier problem. The
first defective gasket is the 25th. The null hypothesis follows a
geometric distribution with mean wait 10, and the alternative is that
the mean wait is greater than 10 (as in Section 8.4, Exercise 17).
Get solution
8.8.10 Find the difference in support of the following hypotheses. Compare with the p-value in the earlier problem. The
first defective gasket is the 50th. The null hypothesis follows a
geometric distribution with mean wait 1000, and the alternative is that
the mean wait is less than 1000 (as in Section 8.4, Exercise 18).
Get solution
8.8.11 Use the method of support to check the following hypotheses. The hypothesis in Section 8.5, Exercise 1.
Get solution
8.8.12 Use the method of support to check the following hypotheses. The hypothesis in Section 8.5, Exercise 2.
Get solution
8.8.13 Use the method of support to check the following hypotheses. The hypothesis in Section 8.5, Exercise 3.
Get solution
8.8.14 Use the method of support to check the following hypotheses. The hypothesis in Section 8.5, Exercise 4.
Get solution
8.8.15
How many standard errors from the mean are the following? What are
the corresponding p-values for a two-tailed test? The support for the
null hypothesis is less than the maximum by 2.
Get solution
8.8.16
How many standard errors from the mean are the following? What are
the corresponding p-values for a two-tailed test? The support for the
null hypothesis is less than the maximum by 3.
Get solution
8.8.17
How many standard errors from the mean are the following? What are
the corresponding p-values for a two-tailed test? The support for the
null hypothesis is less than the maximum by 3.5.
Get solution
8.8.18
How many standard errors from the mean are the following? What are
the corresponding p-values for a two-tailed test? The support for the
null hypothesis is less than the maximum by 4.
Get solution
8.8.19
Follow the steps to show that the support has the simple quadratic
form given in the text. Show that ... (expand the quadratic and
plug in definitions of ...).
Get solution
8.8.20
Follow the steps to show that the support has the simple quadratic
form given in the text. Remove the terms that do not depend on μ and show that the maximum occurs at μ = ....
Get solution
8.8.21
Consider the data in Section 8.4, Exercises 23 and 24. Find the
difference in support of the null and alternative hypotheses. Day 1,
when 7 calls arrive in 1 h while only 3.5 were expected (Section 8.4,
Exercise 23).
Get solution
8.8.22
Consider the data in Section 8.4, Exercises 23 and 24. Find the
difference in support of the null and alternative hypotheses. Day 2,
when 8 calls arrive in 1 h while only 3.5 were expected (Section 8.4,
Exercise 24).
Get solution
8.8.23
Consider again the data on 30 waiting times for 2 types of events
used in Section 8.5, Exercises 21 and 22. ... ... Use
maximum likelihood to estimate the rate λ from the waiting times for type
a. Compare the support for the null hypothesis that λ = 1.0 with the support for the maximum likelihood estimate.
Get solution
8.8.24
Consider again the data on 30 waiting times for 2 types of events
used in Section 8.5, Exercises 21 and 22. ... ... Use
maximum likelihood to estimate the rate λ from the waiting times for type
b. Compare the support for the null hypothesis that λ = 1.0 with the support for the maximum likelihood estimate.
Get solution
8.8.26 In
Exercises 23 and 24, the mean and standard deviation are strongly
affected by extreme values. Exclude the outlier or outliers and
recompute the maximum likelihood estimator of λ. Compare the support for the null hypothesis that λ= 1.0
with the support for the maximum likelihood estimate. Does the
estimator change a great deal? Why does the support become so much
larger? For type b, exclude the extreme values 4.16 and 4.83.
Get solution
8.8.26 In
Exercises 23 and 24, the mean and standard deviation are strongly
affected by extreme values. Exclude the outlier or outliers and
recompute the maximum likelihood estimator of λ. Compare the support for the null hypothesis that λ= 1.0
with the support for the maximum likelihood estimate. Does the
estimator change a great deal? Why does the support become so much
larger? For type b, exclude the extreme values 4.16 and 4.83.
Get solution
8.8.27
Use the method of support to test whether the following samples
differ. One player makes 5 out of 10 shots, another makes 9 out of 10.
Get solution
8.8.28
Use the method of support to test whether the following samples
differ. One player makes 5 out of 10 shots, another makes 16 out of 20.
Get solution
8.8.29
Use the method of support to test whether the following samples
differ. A 1 ... region in Utah is hit by 4 cosmic rays in 1 yr, and a 1
... region at the North Pole is hit by 10 cosmic rays in 1 yr.
Get solution
8.8.30
Use the method of support to test whether the following samples
differ. Two 1 ... regions in Utah are hit by 3 and 5 cosmic rays in 1
yr, and a 1 ...region at the North Pole is hit by 10 cosmic rays in 1
yr.
Get solution
8.8.31
Use
the G test to test the following by building a table complete with
observed and expected values. Compare the G statistic with the
difference in support found in the earlier problem. As in Exercise 27,
one player makes 5 out of 10 shots, another makes 9 out of 10.
Get solution
8.8.32
Use
the G test to test the following by building a table complete with
observed and expected values. Compare the G statistic with the
difference in support found in the earlier problem. As in Exercise 28,
one player makes 5 out of 10 shots, another makes 16 out of 20.
Get solution
8.8.33 One
organism has 8 mutations in 1 million base pairs, a second has 18 in 1
million, and a third has 28 in 1 million. Use the method of support to
test the following differences. Check whether organisms 1 and 2 differ and compare with Section 8.6, Exercise 39.
Get solution
8.8.34 One
organism has 8 mutations in 1 million base pairs, a second has 18 in 1
million, and a third has 28 in 1 million. Use the method of support to
test the following differences. Check whether organisms 2 and 3 differ and compare with Section 8.6, Exercise 40.
Get solution
8.8.35 It
has been proposed that a particular salubrious bath extends cell
lifespan. Suppose that cell mortality follows an exponential model. Use
the method of support to evaluate the following cases. A cell in
the salubrious bath survives 30 min, and a cell in standard culture
survives only 5 min. Is there reason to think that the salubrious bath
lengthens cell life?
Get solution
8.8.36 It
has been proposed that a particular salubrious bath extends cell
lifespan. Suppose that cell mortality follows an exponential model. Use
the method of support to evaluate the following cases. In a
repeated experiment, the cell in the salubrious bath survives 60 min,
and a cell in standard culture survives only 3 min. Is there reason to
think that the salubrious bath lengthens cell life?
Get solution
8.8.37
It
has been proposed that a particular salubrious bath extends cell
lifespan. Suppose that cell mortality follows an exponential model. Use
the method of support to evaluate the following cases. Combine the data
from Exercises 35 and 36, and evaluate the difference in support
between the null and alternative hypotheses.
Get solution
8.8.38
It
has been proposed that a particular salubrious bath extends cell
lifespan. Suppose that cell mortality follows an exponential model. Use
the method of support to evaluate the following cases. What would
happen to the result in Exercise 37 if a third experiment were done and
both cells survived 10 min? Why the change?
Get solution
