8.6.1 ...
Get solution
8.6.2 ...
Get solution
8.6.3 ...
Get solution
8.6.4 ...
Get solution
8.6.5 Find the pooled variance for two populations with the following sample sizes and sample variances. ...
Get solution
8.6.6 Find the pooled variance for two populations with the following sample sizes and sample variances. ...
Get solution
8.6.7
Find the pooled variance for two populations with the following
sample sizes and sample variances. ... Compare with the value in
Exercise 5.
Get solution
8.6.8
Find the pooled variance for two populations with the following
sample sizes and sample variances. ... Compare with the value in
Exercise 6.
Get solution
8.6.9 Find the standard error of the difference of the means in each case. The situation in Exercise 5.
Get solution
8.6.10 Find the standard error of the difference of the means in each case. The situation in Exercise 6.
Get solution
8.6.11 Find the standard error of the difference of the means in each case. The situation in Exercise 7.
Get solution
8.6.12 Find the standard error of the difference of the means in each case. The situation in Exercise 8.
Get solution
8.6.13 Apply a two-tailed t test in the following cases. The situation in Exercise 9 with ...
Get solution
8.6.14 Apply a two-tailed t test in the following cases. The situation in Exercise 10 with ...
Get solution
8.6.15 Apply a two-tailed t test in the following cases. The situation in Exercise 11 with ...
Get solution
8.6.16 Apply a two-tailed t test in the following cases. The situation in Exercise 12 with ...
Get solution
8.6.17 Recall the data in Section 8.5, Exercises 1–4 describing 10 plants in an experimental plot. ... Suppose
that these plants are being compared with populations in a control
plot. Use a two-tailed test, and compare the p-values with those found
in the earlier problem. There are ten plants in the control plot
with mean weight 10.0, and the variance for weight in both populations
is known to be 9.0. Compare with the results in Section 8.5, Exercise 1.
Get solution
8.6.18 Recall the data in Section 8.5, Exercises 1–4 describing 10 plants in an experimental plot. ... Suppose
that these plants are being compared with populations in a control
plot. Use a two-tailed test, and compare the p-values with those found
in the earlier problem. There are ten plants in the control plot
with mean height 36.5, and the variance for height in both populations
is known to be 16.0. Compare with the results in Section 8.5, Exercise
2.
Get solution
8.6.19 Recall the data in Section 8.5, Exercises 1–4 describing 10 plants in an experimental plot. ... Suppose
that these plants are being compared with populations in a control
plot. Use a two-tailed test, and compare the p-values with those found
in the earlier problem. There are 15 plants in the control plot
with mean yield 8.2, and the variance for yield in both populations is
known to be 6.25. Compare with the results in Section 8.5, Exercise 3.
Get solution
8.6.20 Recall the data in Section 8.5, Exercises 1–4 describing 10 plants in an experimental plot. ... Suppose
that these plants are being compared with populations in a control
plot. Use a two-tailed test, and compare the p-values with those found
in the earlier problem. There are 20 plants in the control plot
with mean seed number 15.0, and the variance for seed number in both
populations is known to be 25.0. Compare with the results in Section
8.5, Exercise 4.
Get solution
8.6.21
Consider
again the data in Exercises 17–20, but suppose that variances are
unknown. Use the sample variance for the experimental population found
in the earlier problem and the given sample variance for the control
population to perform a t test on these unpaired populations. The ten
plants in the control plot have mean weight 10.0 and sample variance
8.80. Compare with the results in Exercise 17.
Get solution
8.6.22
Consider
again the data in Exercises 17–20, but suppose that variances are
unknown. Use the sample variance for the experimental population found
in the earlier problem and the given sample variance for the control
population to perform a t test on these unpaired populations. The ten
plants in the control plot have mean height 36.5 and sample variance of
17.2. Compare with the results in Exercise 18.
Get solution
8.6.23
Consider
again the data in Exercises 17–20, but suppose that variances are
unknown. Use the sample variance for the experimental population found
in the earlier problem and the given sample variance for the control
population to perform a t test on these unpaired populations. The 15
plants in the control plot have mean yield 8.2 and sample variance of
8.2. Compare with the results in Exercise 19.
Get solution
8.6.24 Consider
again the data in Exercises 17–20, but suppose that variances are
unknown. Use the sample variance for the experimental population found
in the earlier problem and the given sample variance for the control
population to perform a t test on these unpaired populations. The
20 plants in the control plot have mean seed number 15.0 and sample
variance of 14.2. Compare with the results in Exercise 20.
Get solution
8.6.25 Test the null hypothesis that the means from two populations are equal in the following cases. ...are sample means found from samples with size ...drawn from normal distributions with known variances .... State the significance level of the test. Use a two-tailed test. ...
Get solution
8.6.27 Test the null hypothesis that the means from two populations are equal in the following cases. ...are sample means found from samples with size ...drawn from normal distributions with known variances .... State the significance level of the test. Use a two-tailed test. ...
Get solution
8.6.27 Test the null hypothesis that the means from two populations are equal in the following cases. ...are sample means found from samples with size ...drawn from normal distributions with known variances .... State the significance level of the test. Use a two-tailed test. ...
Get solution
8.6.28 Test the null hypothesis that the means from two populations are equal in the following cases. ...are sample means found from samples with size ...drawn from normal distributions with known variances .... State the significance level of the test. Use a two-tailed test. ...
Get solution
8.6.29 Use
the normal approximation to test the null hypothesis that men and women
have the same opinions in the following cases. State the significance
level of a two-tailed test. Thirty-five out of 50 men believe
that if dolphins were so smart they could find their way out of nets,
whereas 40 out of 50 women believe this.
Get solution
8.6.30 Use
the normal approximation to test the null hypothesis that men and women
have the same opinions in the following cases. State the significance
level of a two-tailed test. Three hundred fifty out of 500 men and 400 out of 500women.
Get solution
8.6.31 Use
the normal approximation to test the null hypothesis that men and women
have the same opinions in the following cases. State the significance
level of a two-tailed test. Thirty-five out of 50 men and 400 out of 500 women.
Get solution
8.6.32 Use
the normal approximation to test the null hypothesis that men and women
have the same opinions in the following cases. State the significance
level of a two-tailed test. Seventy out of 1000 men and 40 out
of 500 women. Why do you think the difference is not significant even
though the samples are very large?
Get solution
8.6.33 Algorithm 8.4 uses ...to estimate the variance under the null hypothesis. Why might it make more sense to use ...,
the proportion in the pooled sample? What is the pooled proportion if
96 out of 200 events occur in the control and 54 out of 100 events occur
in the treatment?
Get solution
8.6.34
Algorithm 8.4 uses ...to estimate the variance under the null
hypothesis. Redo the test using ...How different are the results? Under
what circumstances might it make a larger difference which proportion
was used?
Get solution
8.6.35
Algorithm 8.4 uses ...to estimate the variance under the null
hypothesis. Show that the two-sample test turns into the one-sample test
as ... approaches infinity. What is the null hypothesis about the difference between means?
Get solution
8.6.36
Algorithm 8.4 uses ...to estimate the variance under the null
hypothesis. Show that the two-sample test turns into the one-sample test
as ... approaches infinity. What is the distribution of sample means in the treatment population under the null hypothesis?
Get solution
8.6.37 A
cell is placed in a medium with volume equal to that of the cell. Then
100 marked molecules are placed inside, and after 1 h, 40 are found
inside and 60 are found outside. In a control, protein in the membrane
thought to be involved in transporting the molecule has been removed and
50 out of 100 of the molecules are found inside after the same amount
of time. What is the null hypothesis if the cell with the
transporter in place is compared with the control? What is the null
hypothesis if the treatment is compared with the expectation that
molecules end up inside and outside with equal probability?
Get solution
8.6.38 A
cell is placed in a medium with volume equal to that of the cell. Then
100 marked molecules are placed inside, and after 1 h, 40 are found
inside and 60 are found outside. In a control, protein in the membrane
thought to be involved in transporting the molecule has been removed and
50 out of 100 of the molecules are found inside after the same amount
of time. Find the p-value associated with the comparison of the
treatment with the control, and the comparison of the treatment with the
expectation that molecules end up inside and outside with equal
probability. Why do the p-values differ as they do?
Get solution
8.6.39 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 normal approximation
to test whether the following differences are significant. The difference between the first and second organisms.
Get solution
8.6.40 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 normal approximation
to test whether the following differences are significant. The
difference between the second and third organisms. Why is the
significance level different from that in Exercise 39 even though the
observed difference of 10 mutations is the same in each case?.
Get solution
8.6.41
Consider
the following data on ten patients with viral loads measured under
control conditions, after treatment A, and then again after treatment B.
Use the given test to check whether the treatment has an effect.
... Use an unpaired test to look for an effect from treatment A.
Get solution
8.6.42
Consider
the following data on ten patients with viral loads measured under
control conditions, after treatment A, and then again after treatment B.
Use the given test to check whether the treatment has an effect.
... Use an unpaired test to look for an effect from treatment B.
Get solution
8.6.43
Consider
the following data on ten patients with viral loads measured under
control conditions, after treatment A, and then again after treatment B.
Use the given test to check whether the treatment has an effect.
... Use a paired test to look for an effect from treatment A.
Get solution
8.6.44
Consider
the following data on ten patients with viral loads measured under
control conditions, after treatment A, and then again after treatment B.
Use the given test to check whether the treatment has an effect.
... Use a paired test to look for an effect from treatment B.
Get solution
