11/16/2015
Week 8 Assignment
WebAssign
Week 8 Assignment (Homework)
Current Score : – / 51
Due : Wednesday, November 18 2015 11:59 PM EST
YINWEI LIU
CED 6030, section 02, Fall 2015
Instructor: He Wang
0/2 submissions
1. –/1 pointsBBUnderStat11 10.1.001.
In general, are chisquare distributions symmetric or skewed? If skewed, are they skewed right or
left?
skewed left
symmetric
skewed right
skewed right or left
2. –/1 pointsBBUnderStat11 10.1.002.
For chisquare distributions, as the number of degrees of freedom increases, does any skewness
increase or decrease? Do chisquare distributions become more symmetric (and normal) as the
number of degrees of freedom becomes larger and larger?
increases; no
decreases; yes
increases; yes
decreases; no
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Week 8 Assignment
3. –/1 pointsBBUnderStat11 10.1.003.
For chisquare tests of independence and of homogeneity, do we use a righttailed, lefttailed, or
twotailed test?
twotailed
righttailed
lefttailed
righttailed or lefttailed
4. –/1 pointsBBUnderStat11 10.1.004.
In general, how do the hypotheses for chisquare tests of independence differ from those for chi
square tests of homogeneity? Explain your answer.
The null for independence claims all the variables are independent whereas the null for
homogeneity claims a different proportion of interest from each population.
The null for independence claims all the variables are independent whereas the null for
homogeneity claims an equal proportion of interest from each population.
The null for homogeneity claims all the variables are independent whereas the null for
independence claims an equal proportion of interest from each population.
The null for independence claims all the variables are dependent whereas the null for
homogeneity claims an equal proportion of interest from each population.
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Week 8 Assignment
5. –/9 pointsBBUnderStat11 10.1.011.
The following table shows site type and type of pottery for a random sample of 628 sherds at an
archaeological location.
Pottery Type
Mesa Verde
McElmo
Mancos
BlackonWhite
BlackonWhite
BlackonWhite
Mesa Top
78
58
53
189
CliffTalus
76
73
64
213
Canyon Bench
91
73
62
226
Column Total
245
204
179
628
Site Type
Row Total
Use a chisquare test to determine if site type and pottery type are independent at the 0.01 level
of significance.
(a) What is the level of significance?
State the null and alternate hypotheses.
H0: Site type and pottery are not independent.
H1: Site type and pottery are independent.
H0: Site type and pottery are independent.
H1: Site type and pottery are independent.
H0: Site type and pottery are not independent.
H1: Site type and pottery are not independent.
H0: Site type and pottery are independent.
H1: Site type and pottery are not independent.
(b) Find the value of the chisquare statistic for the sample. (Round the expected
frequencies to at least three decimal places. Round the test statistic to three decimal
places.)
Are all the expected frequencies greater than 5?
Yes
No
What sampling distribution will you use?
chisquare
Student’s t
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Week 8 Assignment
binomial
normal
uniform
What are the degrees of freedom?
(c) Find or estimate the Pvalue of the sample test statistic. (Round your answer to three
decimal places.)
(d) Basedon your answers in parts (a) to (c), will you reject or fail to reject the null
hypothesis of independence?
Since the Pvalue > α, we fail to reject the null hypothesis.
Since the Pvalue > α, we reject the null hypothesis.
Since the Pvalue ≤ α, we reject the null hypothesis.
Since the Pvalue ≤ α, we fail to reject the null hypothesis.
(e) Interpret your conclusion in the context of the application.
At the 1% level of significance, there is sufficient evidence to conclude that site and
pottery type are not independent.
At the 1% level of significance, there is insufficient evidence to conclude that site
and pottery type are not independent.
6. –/1 pointsBBUnderStat11 10.2.001.
For a chisquare goodnessoffit test, how are the degrees of freedom computed?
The number of categories minus two.
The number of categories plus one.
The number of categories minus one.
The number of categories minus three.
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Week 8 Assignment
7. –/1 pointsBBUnderStat11 10.2.002.
How are expected frequencies computed for goodnessoffit tests?
Divide the total sample size by the sample size for each category.
Take the proportion of the sample size for each category designated by the proposed
distribution.
Divide the proportion of the sample size for each category by the total sample size.
Take the proportion of the sample size for each category from the observed data.
8. –/1 pointsBBUnderStat11 10.2.003.
Explain why goodnessoffit tests are always righttailed tests.
We use a χ2 distribution where only smaller values can lead to rejecting the null.
We use a binomial distribution where only larger values can lead to rejecting the null.
We use a χ2 distribution where only larger values can lead to rejecting the null.
We use a normal distribution where only larger values can lead to rejecting the null.
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Week 8 Assignment
9. –/1 pointsBBUnderStat11 10.2.004.
When the sample evidence is sufficient to justify rejecting the null hypothesis in a goodnessoffit
test, can you tell exactly how the distribution of observed values over the specified categories
differs from the expected distribution? Explain your answer.
Yes. When we reject the null, we can only conclude that the observed distribution is
different from the expected distribution.
No. When we reject the null, we can only conclude that the observed distribution is different
from the expected distribution.
Yes. When we reject the null, we can tell exactly how the observed distribution is different
from the expected distribution.
No. When we reject the null, we can tell exactly how the observed distribution is different
from the expected distribution.
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Week 8 Assignment
10.–/9 pointsBBUnderStat11 10.2.006.
The type of household for the U.S. population and for a random sample of 411 households from a
community in Montana are shown below.
Observed Number
Percent of U.S.
Type of Household
of Households in
Households
the Community
Married with children
26%
104
Married, no children
29%
118
9%
30
One person
25%
90
Other (e.g., roommates, siblings)
11%
69
Single parent
Use a 5% level of significance to test the claim that the distribution of U.S. households fits the
Dove Creek distribution.
(a) What is the level of significance?
State the null and alternate hypotheses.
H0: The distributions are the same.
H1: The distributions are the same.
H0: The distributions are the same.
H1: The distributions are different.
H0: The distributions are different.
H1: The distributions are the same.
H0: The distributions are different.
H1: The distributions are different.
(b) Find the value of the chisquare statistic for the sample. (Round the expected
frequencies to two decimal places. Round the test statistic to three decimal places.)
Are all the expected frequencies greater than 5?
Yes
No
What sampling distribution will you use?
Student’s t
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Week 8 Assignment
binomial
uniform
normal
chisquare
What are the degrees of freedom?
(c) Find or estimate the Pvalue of the sample test statistic. (Round your answer to three
decimal places.)
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null
hypothesis that the population fits the specified distribution of categories?
Since the Pvalue > α, we fail to reject the null hypothesis.
Since the Pvalue > α, we reject the null hypothesis.
Since the Pvalue ≤ α, we reject the null hypothesis.
Since the Pvalue ≤ α, we fail to reject the null hypothesis.
(e) Interpret your conclusion in the context of the application.
At the 5% level of significance, the evidence is sufficient to conclude that the
community household distribution does not fit the general U.S. household
distribution.
At the 5% level of significance, the evidence is insufficient to conclude that the
community household distribution does not fit the general U.S. household
distribution.
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Week 8 Assignment
11.–/1 pointsBBUnderStat11 10.3.001.
Does the x distribution need to be normal in order to use the chisquare distribution to test the
variance? Is it acceptable to use the chisquare distribution to test the variance if the x
distribution is simply moundshaped and more or less symmetric?
Yes, it needs to be normal. No, the chisquare test of variance requires the x distribution to
be exactly normal.
No, it does not need to be normal. Yes, the chisquare test of variance allows for the x
distribution to be simply moundshaped or symmetric.
Yes, it needs to be normal. Yes, the chisquare test of variance allows for the x distribution
to be simply moundshaped or symmetric.
No, it does not need to be normal. No, the chisquare test of variance requires the x
distribution to be exactly normal.
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Week 8 Assignment
12.–/11 pointsBBUnderStat11 10.3.004.
Let x = age in years of a rural Quebec woman at the time of her first marriage. In the year 1941,
the population variance of x was approximately σ2 = 5.1. Suppose a recent study of age at first
marriage for a random sample of 31 women in rural Quebec gave a sample variance s2 = 2.5. Use
a 5% level of significance to test the claim that the current variance is less than 5.1. Find a 90%
confidence interval for the population variance.
(a) What is the level of significance?
State the null and alternate hypotheses.
Ho: σ2 = 5.1; H1: σ2 ≠ 5.1
Ho: σ2 < 5.1; H1: σ2 = 5.1
Ho: σ2 = 5.1; H1: σ2 > 5.1
Ho: σ2 = 5.1; H1: σ2 < 5.1
(b) Find the value of the chisquare statistic for the sample. (Use 2 decimal places.)
What are the degrees of freedom?
What assumptions are you making about the original distribution?
We assume a binomial population distribution.
We assume a uniform population distribution.
We assume a exponential population distribution.
We assume a normal population distribution.
(c) Find or estimate the Pvalue of the sample test statistic. (Use 4 decimal places.)
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null
hypothesis?
At the α = 0.05 level, we reject the null hypothesis and conclude the data are not
statistically significant.
At the α = 0.05 level, we reject the null hypothesis and conclude the data are
statistically significant.
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At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are
not statistically significant.
At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are
statistically significant.
(e) Interpret your conclusion in the context of the application.
Fail to reject the null hypothesis, there is sufficient evidence to conclude the
variance of age at first marriage is less than 5.1.
Reject the null hypothesis, there is insufficient evidence to conclude the variance of
age at first marriage is less than 5.1.
Reject the null hypothesis, there is sufficient evidence to conclude the variance of
age at first marriage is less than 5.1.
Fail to reject the null hypothesis, there is insufficient evidence to conclude the
variance of age at first marriage is less than 5.1.
(f) Find the requested confidence interval for the population variance or population
standard deviation. (Use 2 decimal places.)
lower limit
upper limit
Interpret the results in the context of the application.
We are 90% confident that σ2 lies outside this interval.
We are 90% confident that σ2 lies above this interval.
We are 90% confident that σ2 lies below this interval.
We are 90% confident that σ2 lies within this interval.
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Week 8 Assignment
13.–/1 pointsBBUnderStat11 10.4.001.
When using the F distribution to test variances from two populations, should the random variables
from each population be independent or dependent?
independent
dependent
14.–/1 pointsBBUnderStat11 10.4.002.
When using the F distribution to test two variances, is it essential that each of the two populations
be normally distributed? Would it be all right if the populations had distributions that were mound
shaped and more or less symmetrical?
Yes, both populations must be normal. Moundshaped or symmetric distributions will
qualify.
No, the populations do not have to be normal. Moundshaped or symmetric distributions do
not qualify.
No, the populations do not have to be normal. Moundshaped or symmetric distributions will
qualify.
Yes, both populations must be normal. Moundshaped or symmetric distributions do not
qualify.
15.–/1 pointsBBUnderStat11 10.4.003.
In general, is the F distribution symmetrical? Can values of the F distribution be negative?
Yes; No
Yes; Yes
No; No
No; Yes
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16.–/1 pointsBBUnderStat11 10.4.004.
To use the F distribution, what degrees of freedom need to be calculated?
Only the degrees of freedom for the numerator need to be calculated.
Only the degrees of freedom for the denominator need to be calculated.
The degrees of freedom for both the numerator and denominator need to be calculated.
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Week 8 Assignment
17.–/9 pointsBBUnderStat11 10.4.012.
A new thermostat has been engineered for the frozen food cases in large supermarkets. Both the
old and new thermostats hold temperatures at an average of 25°F. However, it is hoped that the
new thermostat might be more dependable in the sense that it will hold temperatures closer to
25°F. One frozen food case was equipped with the new thermostat, and a random sample of 26
temperature readings gave a sample variance of 5.1. Another similar frozen food case was
equipped with the old thermostat, and a random sample of 19 temperature readings gave a
sample variance of 12.2. Test the claim that the population variance of the new thermostat
temperature readings is smaller than that for the new thermostat. Use a 5% level of significance.
How could your test conclusion relate to the question regarding the dependability of the
temperature readings? (Let population 1 refer to data from the old thermostat.)
(a) What is the level of significance?
State the null and alternate hypotheses.
H0: σ12 = σ22; H1: σ12 > σ22
H0: σ12 = σ22; H1: σ12 ≠ σ22
H0: σ12 = σ22; H1: σ12 < σ22
H0: σ12 > σ22; H1: σ12 = σ22
(b) Find the value of the sample F statistic. (Round your answer to two decimal places.)
What are the degrees of freedom?
dfN =
dfD =
What assumptions are you making about the original distribution?
The populations follow dependent normal distributions. We have random samples
from each population.
The populations follow independent normal distributions. We have random samples
from each population.
The populations follow independent chisquare distributions. We have random
samples from each population.
The populations follow independent normal distributions.
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(c) Find or estimate the Pvalue of the sample test statistic. (Round your answer to four
decimal places.)
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null
hypothesis?
At the α = 0.05 level, we reject the null hypothesis and conclude the data are not
statistically significant.
At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are
statistically significant.
At the α = 0.05 level, we reject the null hypothesis and conclude the data are
statistically significant.
At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are
not statistically significant.
(e) Interpret your conclusion in the context of the application.
Reject the null hypothesis, there is sufficient evidence that the population variance
is smaller in the new thermostat temperature readings.
Fail to reject the null hypothesis, there is insufficient evidence that the population
variance is smaller in the new thermostat temperature readings.
Fail to reject the null hypothesis, there is sufficient evidence that the population
variance is smaller in the new thermostat temperature readings.
Reject the null hypothesis, there is insufficient evidence that the population variance
is smaller in the new thermostat temperature readings.
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