# CED 6030, section 02, Fall 2015 Week 8 Assignment (Homework)

August 30, 2017

Question
11/16/2015 Week 8 Assignment
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12678647 1/15
Current Score : – / 51 Due : Wednesday, November 18 2015 11:59 PM EST
0/2 submissions
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
1. –/1 pointsBBUnderStat11 10.1.001.
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
2. –/1 pointsBBUnderStat11 10.1.002.
Week 8 Assignment (Homework)

CED 6030, section 02, Fall 2015

WebAssign
11/16/2015 Week 8 Assignment
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12678647 2/15
For chi­square tests of independence and of homogeneity, do we use a right­tailed, left­tailed, or
two­tailed test?
two­tailed
right­tailed
left­tailed
right­tailed or left­tailed
3. –/1 pointsBBUnderStat11 10.1.003.
In general, how do the hypotheses for chi­square tests of independence differ from those for chisquare
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.
4. –/1 pointsBBUnderStat11 10.1.004.
11/16/2015 Week 8 Assignment
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12678647 3/15
The following table shows site type and type of pottery for a random sample of 628 sherds at an
archaeological location.
Pottery Type
Site Type
Mesa Verde
Black­on­White
McElmo
Black­on­White
Mancos
Black­on­White
Row Total
Mesa Top 78 58 53 189
Cliff­Talus 76 73 64 213
Canyon Bench 91 73 62 226
Column Total 245 204 179 628
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
5. –/9 pointsBBUnderStat11 10.1.011.
11/16/2015 Week 8 Assignment
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12678647 4/15
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) Based on your answers in parts (a) to (c), will you reject or fail to reject the null
hypothesis of independence?
Since the P­value > ?, we fail to reject the null hypothesis.
Since the P­value > ?, we reject the null hypothesis.
Since the P­value ? ?, we reject the null hypothesis.
Since the P­value ? ?, 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.
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.
6. –/1 pointsBBUnderStat11 10.2.001.
11/16/2015 Week 8 Assignment
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12678647 5/15
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.
7. –/1 pointsBBUnderStat11 10.2.002.
Explain why goodness­of­fit tests are always right­tailed tests.
We use a ?2 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 ?2 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.
8. –/1 pointsBBUnderStat11 10.2.003.
11/16/2015 Week 8 Assignment
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12678647 6/15
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
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.
9. –/1 pointsBBUnderStat11 10.2.004.
11/16/2015 Week 8 Assignment
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12678647 7/15
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.
Type of Household
Percent of U.S.
Households
Observed Number
of Households in
the Community
Married with children 26% 104
Married, no children 29% 118
Single parent 9% 30
One person 25% 90
Other (e.g., roommates, siblings) 11% 69
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
10.–/9 pointsBBUnderStat11 10.2.006.
11/16/2015 Week 8 Assignment
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12678647 8/15
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 > ?, we fail to reject the null hypothesis.
Since the P­value > ?, we reject the null hypothesis.
Since the P­value ? ?, we reject the null hypothesis.
Since the P­value ? ?, 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.
11/16/2015 Week 8 Assignment
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12678647 9/15
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.
11.–/1 pointsBBUnderStat11 10.3.001.
11/16/2015 Week 8 Assignment
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12678647 10/15
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 ?2 = 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: ?2 = 5.1? H1: ?2 ? 5.1
Ho: ?2 5.1
Ho: ?2 = 5.1? H1: ?2 ?2
2
H0: ?1
2 = ?2
2? H1: ?1
2 ? ?2
2
H0: ?1
2 = ?2
2? H1: ?1
2 ?2
2? H1: ?1
2 = ?2
2
(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.
17.–/9 pointsBBUnderStat11 10.4.012.
11/16/2015 Week 8 Assignment
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=12678647 15/15
(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 ? = 0.05 level, we reject the null hypothesis and conclude the data are not
statistically significant.
At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are
statistically significant.
At the ? = 0.05 level, we reject the null hypothesis and conclude the data are
statistically significant.
At the ? = 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.

Get a 30 % discount on an order above \$ 5
Use the following coupon code:
CHRISTMAS
Positive SSL